Blue can tap for mana with restrictions, right?

Yeah, that's right. I personally wonder whether this restriction is a little loose. I imagine something like this for a set with level up.

This is a reference to Training Grounds, isn't? Maybe it should state straight up that it can only be used for activated abilities of creatures?

Currently it looks a lot better than Thran Turbine for example. That card has a considerable high gatherer rating... Does anybody know whether it's broken or something? Though obviously that depends a lot on the other cards that coexist with it in the environment.

To be honest, I either didn't know it I forgot that Thran Turbine existed.

I doubt it's widely known card - I for one have never seen it in irl, and as I mentioned before, I don't know if that automatically means that this design is unacceptable. Turbine is roughly two decades old after all.

I think the acceptability of this card depends on the environment it would be printed for. For what purpose would it be in the set and so on. The restriction is indeed rather loose so I do think it would have to be "justified" in one way or another.

Blue can certainly power up artifacts; and we've seen it for creature abilities too. So the only remaining possible dodginess on permanents is activated enchantments - which seem eminently a sensible use for it and planeswalkers; which don't have mana cost activations. And blue can certainly mess with alternate costs on stuff; so using the maa for flashback or whatever would be fine.

About the only reason I think they probbly wouldn't make this, and instead make something that's a bit more focussed on whatever that particular set did, is to leave themselves room to make the other variants later. Once this exists, it's had to justify making a more restiricted version later; and people will just clamour for a reprint.

Actually, one reason they might not print this is because of how confusing it is what counts as casting a spell and what doesn't. Flashback is casting so you can't use this on it, but embalm and unearth aren't so you can.

But I don't think that's a deal-breaker. Plenty of rares and some uncommons have effects that trigger on, or prohibit, casting spells or activating abilities.