Mana abilities are kind of weird, and have been so throughout the history of Magic.
If you've ever looked at certain very old cards, you might have noticed that everything that wasn't a land told you something special about its mana ability; prior to Mirage, you played mana abilities of nonland permanents "as an interrupt," and from Mirage up until the release of Sixth Edition, they were played "as a mana source." What were these and why?
So, as you know by now, mana abilities don't use the stack... usually. A very few things can generate mana on resolution that do use the stack, but they are technically not considered mana abilities and can be responded to, etc., as normal. Usually these are things that have restricted timings, such as planeswalker loyalty abilities (Chandra, no matter how much she wants to, cannot suddenly use her loyalty abilities at instant speed - and even that wouldn't be good enough, which I'll talk about in a bit). These riders are an attempt to underscore that this is true because, while it was definitely so for lands, it was not obvious for other permanents. Permanents' abilities were always played at instant speed, and...
Okay, that probably doesn't help too much. So, before the type was removed in Sixth Edition, there was a third one-shot spell type: Interrupt. Interrupts were comparatively few and were reserved specifically for spells that were meant to interact with other spells. This was usually stuff like counterspells, but a few other cards used the type. Notably, text-altering effects, color-changing effects, spell-copying effects, and Ritual effects. The reason for the first three is that, back in the day, Magic operated on a "batch" system, which was similar to the stack, but with speed levels. This caused interrupts to go off first when everybody had passed priority without adding any new effects. It was still first-in-last-out at each speed level, but with a few bits of nuance to differentiate it from the modern stack. There's probably a lot more to go into here, but the short version of it goes this way: if you tried to kill my creature with Terror, but I turned it black with Deathlace, then you tried to cast another Terror, the Deathlace goes off first, because it's faster, causing neither Terror to take effect. Burst mana production stands out in a way, but it's mostly to allow you to play more cards. They're still a type of interaction, and it's primarily to imitate the fact that you could tape lands basically whenever you pleased. (Mana burn was a thing back then, so there were many circumstances under which it was not recommended.)
As such, most abilities were instant-speed, because there was little call for interrupt-speed abilities outside of certain specific circumstances.
Because most activated abilities did not interact with card text or color, nor did they counter, they could comfortably remain at instant speed. In fact, it was often useful for them to do so, e.g. for Circles of Protection, so the various instant-speed effects could concretely subvert them. If it weren't for this distinction, blue players' opponents could simply reactivate their Circles of Protection when they get hit by Sleight of Mind (assuming they weren't tapped out, anyway). Lands' mana abilities, meanwhile, were already that fast, so it was necessary for other permanents to say that their abilities matched interrupt speed, to maintain parity with lands.
Briefly, for about two years, though, these abilities were promoted to a new card type: Mana Source.
Mana Sources were, more or less, just interrupts. This was mostly just a special category of interrupts - however, according to this very old website, containing some rules info from the Mirage rulebook (which I sadly no longer have a copy of - I used to about fifteen to twenty years ago, but I lost it, and they're frankly too expensive for what they are these days), mana sources could not be interrupted. Back then, counterspell wars were totally viable as they are today. This part about mana source spells being uncounterable has not carried over in the rules. Arguably this is probably a power level erratum, but I don't know how frequently this has mattered over the years. If you've ever lost a game of Magic because your Dark Ritual got countered, well, that sucks, buddy. I'd tell you to write it below, but I don't keep a comments section on this website and never intend to.
As such, mana sources were arguably a bit superfluous, and they sure didn't make sense when WotC flattened the rules to use the version of the stack we know today... which wasn't exactly what they did in Sixth Edition, where there were still some oddities (like combat damage using the stack, which is beyond unintuitive). But they did axe the interrupt type and the mana source type. So now all those spells were back to being instants, and the idea of the mana ability was born. No more was the need to have any sort of rider on these abilities. They happened and could not be responded to nor copied. Finally, everything is simple and easy to understand.
Wait, no, hold up, it gets weird again.
Exactly four black-bordered cards have an ability that says "activate only as an instant." Under normal circumstances, this is a useless stipulation, but it matters for mana abilities. Obviously, this is only attached to mana abilities, including what I have to think are two of the most well-known mana cards in Magic, albeit from opposite ends of the spectrum: Lion's Eye Diamond, an infamous combo enabler; and Rhystic Cave, quite possibly the worst land to ever produce one mana of any color. So, what's the deal? Even looking at the old text for Lion's Eye Diamond doesn't seem to reveal anything; isn't this just a modern translation of the rider on the old card?
Er... not quite. Casting a spell is usually something that is simplified greatly in casual play, but it's a fairly complicated thing if broken down. After announcing that you will cast a spell, you pay its mana. Here you're allowed to activate mana abilities and spend mana that you've created otherwise. This happens faster than instant speed, which locks those four cards out of being used after announcing a cast but before payment has finished. The reason for this is to prevent a circumstance where you announce that you are going to cast a spell, but become unable to pay for it. Charmed Pendant features the simplest version of this (well, okay, arguably the two silver-bordered cards' versions are much simpler, but it's the same concept); you're gambling1 to generate mana. You might not have enough mana to cast the spell you're about to cast. If you were hoping to mill that Khalni Hydra so you could play your resident Big Dumb Object, but you whiff and hit a land, well, so much for that. Rhystic Cave shows off another version of this issue. In this case, your opponent can effectively counter your Rhystic Cave mana by paying one generic mana. Again, if that was the last mana you needed to cast your big spell, you've now run into a situation. You can't cast the spell, and because you've possibly given otherwise hidden information to your opponent (i.e. a spell you intend to cast, which is most likely happening from the hand), you've created a game state that can only be rewound from if your opponent is forgetful.
But Lion's Eye Diamond... that one is special. (And I guess Diamond Lion, but it has the same ability.)
See, Lion's Eye Diamond, without this restriction, would have a strong potential to create a different type of scenario where you can't cast your spell - one where you're attempting to cast it from the hand while it's in the graveyard. This would, of course, be highly illegal. Even if the card has a cost to cast it from the graveyard, you must declare that you're paying that alternate cost. Even if it's the same! For some of these cases it really only makes vague mechanical differences, but the basic idea is that it prevents you from casting a spell that you've already discarded to the Diamond's own cost. It's a very strange ability, from a technical stance. It kind of breaks the game in a non-power-level way. I mean, from a power-level perspective, it also breaks the game, but...
Additionally, mana abilities do not have targets. Abilities that target are not mana abilities. This results in a few strange abilities, which (mostly) make players add mana. First, let's talk about Spectral Searchlight, a very weirdly-worded card. In order to stay a mana ability, the ability cannot target. I suuppose there are other reasons to not want it to target - it allows you to pierce True Believer, which, at the time, means that you could use Spectral Searchlight to nearly force one damage on an opponent with True Believer or other targeting-protection effects via the now-retired mana burn rules. Nowadays, it's almost meaningless, unless you're in a team game or doing some very unusual politics.
Secondly, a small amount of cards add mana without being mana abilities. Perhaps most notable is Radiant Lotus, but Valleymaker does this too (also being a former burn-through-shroud card, meaning that until mid-2009, it was a souped-up Heartwood Giant if youu wanted to do that instead of ramping). Bigger on the Inside also grants an ability that adds mana but is not a mana ability.
So, yes. Mana abilities have had some weird history. But as the game has gone on, they've been normalized, probably because there was no reason for them to be weird. Imagine if they stayed regular activated abilities that could be countered by interrupt effects (by virtue of being "played as interrupts") - could you counter them with something like Voidslime in this weird parallel future? Who could possibly even know.
As for why I thought about this... well, it was that recently-released nostalgia-themed Secret Lair. Simple as. But, I guess I just think about the old days of Magic a lot.
1. ↑ Yes, yes, except in the circumstances where you're not. The rules don't care because they need to be as one-size-fits-all as possible.