EDIT -
After watching some youtube videos it is clear that the AR coating is on the user-facing side of the screen, not the inward-facing side, because it is evidently possible to remove the entire coating with some polishing compound and solvent, which makes the screen appearance uniform again. I'll keep my fingers crossed that my display won't have any issues, but at least I know there is an alternative to having the entire screen replaced, possibly multiple times.
I had a 2014 rMBP which had this issue big time. TBH, I did use a screen cleaner, and that is apparently what causes the oleophobic coating to come off. I switched to water when the missing coating was only around the bezel, but it still migrated and eventually spiderwebbed throughout the screen. The replacement screen never exhibited any issues, but I've only used water since.