Not breaking at all. Heck, alchemists get to use crafting, and a class feat can be used to make Nature the skill check. You should probably look at Herbalist archetype for wording.

I don't know of a feat that does that, but I strongly doubt this would be a balance concern. Treat wounds and battlefield medicine are pretty limited anyway, and certainly aren't game-breaking. I'd draw a comparison to bards' Hymn of Healing, which amounts to free, unlimited healing with a 10-minute-per-8-hp-per-2-levels use timer, and also costs a single feat to obtain.

Assurance: Medicine precludes the need to roll altogether, and honestly is a near-mandatory pick for the tabletime it saves. You might save a little in-universe time by manually rolling with a high modifier, but unless your campaign is running at breakneck pacing, the difference isn't worth the real time spent. Recall Knowledge checks with medicine are the only reason I'd want to manually roll, and Anatomy Lore covers a huge swathe of that subject anyway.

All that to say, ehhhh its probably fine to brew up that Medicine->Anatomy Lore feat. I wouldnt reccomend doing something similar for any other skills though.