Why though?

I realize this is most likely pretty parasitic, since there are only 67 cards this would be relevant for (at least per a cursory scryfall inquiry); also it possibly breaks some things, like ice cauldron and lord of the forsaken. And frankly I can't really figure out if it is unplayable or busted. I also realize that it doesn't really fit flavourwise. The ability costs " or 2 life" since I didn't want it to cost outright and I figured that if it could only be payed with mana then there would be even less cards that could possibly want this on the board. Another problem is that I'm not exactly sure how this would work with things like cavern of souls; if I use the cleansed mana from the cavern to cast a creature of the chosen type, would it be counterable?

As written - I think so. It's only removing the restriction - the "that spell can't be countered" clause won't be affected by it.

I agree this is kind of an oddball card that probably won't see much use, most players will just ignore it. But it presents a pleasing puzzle-box, and some people will really enjoy using it. Go for it.

My gut-instinct is that it seems way too costly for it does. I would lower its cost to 1 or perhaps to 2 along with cantripping - so like Prophetic Prism almost. That way people can mess with it and Jeweled Lotus in legacy.

Then again, this is a custom set, so it really ought to do something here specifically rather than in some hypothetical environment. Otherwise, it's just a blank card. You should think what sort of interactions you might want to see with it and then create some cards that more or less by 'fortunate happenstance' benefit from it - then balance it upon those interactions rather than anything else. As is, currently there are zero cards in the set that would benefit from mana cost restrictions being removed, so it might as well cost really.