I think it might even be crucial for bitcoin to increase the cap. psychology of having 0.000000000000001 of a coin aside, there's a very real problem with compensation for miners. Will there really be enough transaction volume to cover mining expenses? By the time the mining rewards become insignificant, the infrastructure around bitcoin will probably be a lot better, and there will be companies like coinbase and xapo that will have bitcoin transactions within its own environment and off chain, to allow micro transactions (so that a 1000 satoshi payment won't require 10000 satoshi transaction fees for example) and to simply save on transaction fees. We don't know how many transactions will actually be done on the blockchain.
If the miner rewards are too low at that time, the bitcoin network will not have enough security and there will inevitably be people who want to destroy it given the chance.
It will depend on some factors such as mining reward, bitcoin price, hashing power, bitcoin adoption etc before the end of bitcoin mining. No one knows it yet! But IMO it is a crazy ideal, which definitely will crash the price. One day bitcoin is popular and the number of it in the circulation cant meet the reqirement of our need, and it falls in to deep deflation. We might need to increase the 21m cap. But who knows now? If the miner rewards are too low at that time, the bitcoin network will not have enough security and there will inevitably be people who want to destroy it given the chance.
