The problem with not having magical healing isn't the raw HP values. You have still access to short and long rests, Purple Dragon Knights, healing kits, arguably healing potions, and feats to augment most of that. Preventing people from bleeding out will require more effort, but that's also true of a normal magic game where nobody bothers to be a healer, which is not an uncommon group composition.
The real problem is curing everything else:
Finding a non-magical analog for Lesser Restoration and Greater Restoration is mandatory.
Finding an analog for Revivify will help cover up the sore spots where players just get unlucky, but it will strain verisimilitude if used often.
Figuring out how to handle the lack of Regenerate will send you looking for prosthetics or retiring characters.
Non-Magical damage resistance can be worked around. In addition to special materials, Magical ammunition and Moon-Touched swords would go from being low tier rewards to extremely valuable while not mechanically impacting too much.