I have 2500hrs and have flown over 30 types of aircraft. I am also a A&P. I have never seen a POH, manufacture or FAA suggestion for wear limits of a tire. The flight school I got my pilots license (1980), would wear the tires of Cessna training aircraft bald on the outside of the tire and flip them on the rims, then run then bald on the opposite side. On airliners and transport aircraft I have seen chunks of rubber missing, cord and belts exposed, etc more so on freight than passenger aircraft. Surely there must be some standard or legal requirement.
( I have seen FAA, mfg, and other info prohibiting flight if tire pressure exceeds +-5%)