Well, that's so true that once BTC reached its max supply, miners will only rely on their gain from transaction fees. Transaction fee at that time might be 15-20 BTC from this
chart in the past 4 month or might be less than 15 BTC once every client implements and used Segwit.
And once all 21M BTC have been mined which is around the year 2140, the supply cannot increase, regardless of growing demand. So as far as the law of supply and demand goes, people assumed that btc price will be much higher than we expected. So even miners will only rely on transaction fees it will be enough to them if the price will reach 5 digits or much better if it breaks until 6 figures, if and only if the demand grows at that time, else, btc and its technology will die.