Yeah, by that time tx fees will greatly outweigh the subsidy. Both go to the mining pool operator, who disperses the Bitcoin. There are ways of getting this pretty cheap; batching the sending, which is already done, but maybe they can release the coins from a few days of mining by keeping track of contributed hash and dispersing in proportion. Opening a LN channel with each miner is also a possibility.

Since mining pools compete with each other and switching pools is easy, the pools that innovative to get the most sats/work in the miner's wallet wins the hashpower.