(Un)Fortunately, this will happen much sooner than once we mine the 21,000,000th coin. Looking at the graph, in 2040, every block will reward only 0.1953125 bitcoins, so you should consider that it may be more profitable to gain all the transaction fees, than the block reward, before 2140.

Whether it'll be more profitable or not, this proof of work competition (AKA mining) is made in a way to always work. It'll never stop. If the 0.19 BTC aren't enough for covering miners' expanses, then they'll stop mining. This will result on difficulty decrease which will then be profitable for some miners, with fewer expanses! The only terrifying thing to think is the total transactions in the mempool, because after all, that's bitcoin.