Each transactions has a fee value set by the sender, that goes to the miner. Miners select the top N transactions by fee, so miners will still have an incentive.

The fees are already exorbitant and make no sense if you wanted to use Bitcoin for everyday transactions. You still see merchants that have something like a 2$ minimum for credit card transactions, which charge a percentage fee usually.

Looking at https://ycharts.com/indicators/bitcoin_average_transaction_f... the average Bitcoin fee seems to be somewhere around $22 right now. Just think of the dialog occurring once miners have to make all their money from fees only:

"Yes sir, I would like to buy this chewing gum for my son. Yes I know it costs $0.50. Yes I know it will cost me the equivalent fee of $50 to buy it using Bitcoin. Now sell it to me already!".

True. Bitcoin as currently designed doesn't support the transaction throughput or latency anyways for folks to buy gum, only larger money transfers. (I'm a skeptic, FWIW)

Without the presence of transaction fees though, things would fall apart once the block reward ran out, as asked in the original question.