this actually a simple answer but very true.
but in my opinion the bitcoin will pretty much still exist maybe there will be debate when the supply is near to the limit and maybe there will be fork of bitcoin that pop off. but the miner will still be there to receive the transaction fee.
You are absolutely right. Miners will continue receiving reward in the shape of transaction fee even after all the Bitcoins are mined and as the Bitcoin adaption grows over time, their revenue will increase but transaction speed will be much higher compared to what it is now due to technological development. The scarcity due to no more supply of Bitcoin will increase the price to new highs. This is my opinion based on how I perceive future of Bitcoin and thing can happen totally opposite. It is better to do your own research before taking any investment decision.