Bitcoin limited supply issue

As everyone knows, there will always ever be 21 million bitcoins. And every 4 yeats, mining rewards will become smaller and smaller. What if bitcoin's price fails to keep up with rewards shrinking? What happens when every bitcoin is finally mined? After all this there will probably be way less miners securing the network without being incentivized by block rewards (eventually centralizing the network). If miners still wanted to be profitable they would have to rely on transaction fees, this means bitcoin will keep getting more expensive. What do you think about this?