Can a miner give themselves less than the maximum block subsidy if they wish to do so?
Yes, it would have. In fact, this has happened before in many different blocks.

The Bitcoin wiki has two instances of this documented:


  In block 124724, user midnightmagic solo mined a block which caused one less Satoshi to be created than would otherwise have come into existence. Therefore, all calculations from this block onwards must now, to be accurate, include this underpay in total Bitcoins in existence. Then, in an act of sheer stupidity, a more recent miner who failed to implement RSK properly destroyed an entire block reward of 12.5 XBT in block 501726.