Yes, miners will receive transaction fees. But have you run the numbers on how much those transaction fees would have to be to match the current block reward?
The endgame seems completely untenable. No one is going to pay a huge amount per BTC transfer. So what do you think will happen to all those miners, with all their mining equipment?
We currently have a monstrous block reward every 10 minutes, and yet tx fees are already $10 to $20. Imagine how much the fees will be when there's no reward.