When someone's learning, it's better to start them off with only what they absolutely need to know, and then present them with new information only once it becomes relevant. Teaching players about all the nitpicky exceptions to "mana abilities are abilities that produce mana" as soon as we clear up their initial confusion violates this principle--such cards are rarely encountered, and the differences matter even more rarely. But if we don't do that (or if we forget, which also happens), then we have a player who's been given instruction that they aren't aware is incomplete, so later attempts to educate them are going to run into the instinctive response of "But that's not what I was told!". They may accept the correction, but they also might not.
With a more precise name, the player is ahead of the game--they can proceed without any instruction at all, so when they eventually do encounter a situation where the difference matters, they don't have that incomplete instruction barrier, and can be taught "fresh".
I'm not convinced that a "that's not what I was told!" reaction is worse than a "that's not what it says!" reaction. you may be right that you don't want to dive into all the details, but by the time you come to mana abilities in the first place, you're already looking at some non-simple cards. there are only 44 cards with either "mana ability" or "mana abilities" on them, mostly in the reminder text of split second and cards that target activated abilities. either way, it's not something you'll encounter until you've played for a bit. and you don't have to explain everything, just toss in a "with a few exceptions" so that, when they encounter one, they'll go "oh hey this is one of those exceptions" not "NO WAY DUDE"
Maybe, but I think the benefits of an intuitive name outweigh the drawbacks. Making the fact that it's an artificially constructed subset feel reasonable is irrelevant if you never need let them know that that's what it is.
but you will. at some point, you're going to try to activate
deathrite shaman for mana in response to a
sudden shock, and boom, everything falls to pieces and you get into an argument that escalates into a fist fight, get permanently injured, get fired from your job because you can no longer do it, and wind up in a gutter somewhere, begging for change, all because Zammm wanted to add an extra word to some magic cards. do you see what you've done? how could you?
more relevantly, while it doesn't come up often, it does come up, and making it more intuitive when it does is a good thing. also, a much more likely example would've been
tormod's crypt in response to shaman, but that also requires you to know that mana abilities don't use the stack, and doesn't actually use the term "mana ability" anywhere.
On the contrary, I think that a player who's been playing Magic on a serious enough level to encounter a situation where the messy behind-the-curtain rules regarding mana abilities become relevant is more likely to accept such a lesson than one who hasn't. Experienced and/or serious players are much more aware that they don't know all the nitty-gritty details, and are used to accepting the word of authority figures on how the rules work.
It's the inexperienced and casual players who are more likely to resist instruction. Happily, they're also the ones least likely to encounter situations where it matters.
you can't really juxtapose "experienced" with "casual" like that.
lemme anecdote ya. so I switched high schools in tenth grade. one of the first ways that I connect with people is through magic. (I had a truly awful deck that tried to be five-color with only forests and ran all the invasion Apprentices and Masters because I had no clue what I was doing, but that's neither here nor there.) there was a kid who had a mono-colored deck of each color, and a lot of people just borrowed his decks to play quick matches. the red deck contained
onslaught. now, these are people who'd been playing for possibly close to a decade in some cases, and people who'd been to tournaments, and literally none of them believed me when I explained that and why
onslaught's trigger could target an already tapped creature, so that you didn't have to tap your own creatures to play
ball lightning if you'd already tapped down their creatures. not one person listened. in the end, I had to print out I believe the gatherer rulings but it may have been the relevant comp rule sections before anyone would believe me. why? because the authority figure they had was wrong. I was a new guy, no one knew that I knew what I was talking about, so why should they listen to me? that's gonna be a lot of players' expositions to misinterpreted rules. and as you say, it's not a common thing to come up, so even if players had been to tournaments they might not have experienced the scenario. of course, this is going to happen either way, (there's really nothing they could've done to prevent the onslaught issue, for instance.) but I believe people will be less hardline about it if the terminology is a little more vague, so that one can prevail with reasoned arguments without running so much into the brick wall of "the card literally says 'mana producing', this ability produces mana, what the heck are you talking about."