If Bitcoin could be mined forever with the halvings disappearing at some point and the rewards remaining the same after that forever, I don't think it would be a major problem. While there would be more and more BTC, the rate at which more of them become available would allow a certain stability. Okay, maybe Bitcoin would then be susceptible to inflation, but the rate could remain very precise because of this limitation on the BTC that can be mined.
I think Monero got this right - an eternal and low rate of inflation once the big stuff is out of the way. If I were designing something I wanted to be used as a currency I wouldn't have a hard cap on supply. It's great for those who want to make money, less so if you want it to be money.
It would be interesting to still be chugging when this becomes a pressing issue, or perhaps it'll be so set in stone by the time halvings end and the fee market proves to be workable that it won't ever be questioned.