I think the block reward is going to become an irrelevance well before 2140.

The miners are currently collecting fees of 0.3-0.4 coins per block, and it's rising over time. And this amount is what the block reward will be in about twenty years time. So the cross-over point (when fees outstrip block rewards) is probably going to come sooner than then - and most of us will still be alive.

It might happen that 2nd layer stuff (payment channel networks such as lightning) and block size increases (which few will be able to argue against as network rates and storage capacity get higher) will exert a downward pressure on fees. But despite this, as demand increases I'm sure the fees will increase well beyond the current value if bitcoin manages to remain the most strongly backed crypto-currency.