Wisdom-less, magic-less healing?

If I understand this correctly one could build a character with assurance in medicine and just automatically succeed any typical Treat Wounds or Battle Medicine at 3rd level, assuming Trained in Medicine. Adding Godless Healing grants bonus healing and more frequent Battle Medicine, at least on yourself, and Mortal Healing at the next level means you basically crit succeed any of these checks... For free. It seems like the increased DC versions of Treat Wounds at higher proficiencies scale pretty closely with the auto-roll from Assurance, too; so there's some mostly-free bonus healing (with the cost being the training Medicine instead of other skills).

Is it just me or does this mean one could build a pretty decent non-magical healer without dropping a single point into wisdom? Is there something about these actions/feats that I'm missing?