The "problem" (if it is indeed one) will have appeared long before 2140.
After 3 more halvings, the block reward will be less than 1 btc, and after another 3, it will be less than 0.1.
So in the next 20-25 years, it will be comparable to current transaction fees.

It's an unpopular opinion, but I don't think having a constant block reward of, say 1 btc after sufficient halvings would have been a bad idea. Inflation would be minimal and predictable.
But I do think it's too late now to implement it as it would do more harm than good, due to FUD as it would be painted as a betrayal to the golden initial rules. So It's a moot point.

Still, after 20 years I expect most daily transactions to have crossed over to the lightning network, leaving layer 1 just for settlements, opening and closing channels, or exceptional, large and costly transactions.
I think it's totally sustainable if the ecosystem is strong.