You forgot the Eldritch Knight and Spellthief in your first category as well... you know the actual fighter (& thief) who spent resources and made choices (narrative and mechanical) to gain access to magic... but you know...details.
Don't recall either getting access to healing spells. Really, though, it's all classes all the time, since everyone can buy a healer's kit and thereby just crush the niche protections. Just crush.
But, that aside, you've done a bit of goal post shifting here. I was responding to the niche protection argument, and showing that that niche is so broad that it's pretty much baseline, but you've responded with a different argument about resources invested. However, the question asked in the OP is parallel to something that requires no real investment at all -- a healer's kit, or multiple feats, or a cantrip. The difference is that the fighter has to attempt the effort with no guarantee of result -- all of the responses allowing it have failure as a possibility, while the others are fiat abilities that just work without risk of failure. Buy a healers kit -- works. Use the Healer feat -- works. Use a cantrip -- works. Use a higher level resource -- works and better.
You're claiming that a mere chance as something that another class can do with a minimal resource without risk is somehow so terrible that it risks unbalancing the resource game and the niche protections. I just don't see it. You clearly have no issue with the fighter's shtick of melee or ranged combat being totally shared out, often better, to other classes.
Actually do we even need those two classes since their main differentiating subclass ability could just be replicated with a skill roll by any other subclass? In fact if a regular fighter can both declare his connection to a sorcerous bloodline and pray for divine aid... he has access to more varied and better magical spells so is arguably better than either.
It's replicated by a host of other classes and things. And they're fiat abilities for those characters -- they get to do them and have the work. The fighter trying to declare as you posit here, is not guaranteed anything even if the attempt is allowed. You're arguing against the chance, and assuming that allowing the chance means parity. I'm not sure where you get that from.