On BTC the word "fee" is a misnomer.
A "fee" is a payment for a service. With a "fee" the amount is typically stated in advance, and when you pay, it constitutes a good faith assurance that the service will be performed.
That's not what we have at all on BTC.
On BTC when blocks become full, "fees" can become wildly unpredictable. since every transaction is competing with all backlogged and arriving transactions for space in the next block, inclusion in the next block requires guessing an amount that's higher than the bids of roughly the 3000 highest bidders in that round. there is no way to reliably predict inclusion in the next block. if you guess too low, and the backlog is growing, your transaction may never confirm.
What we have here is not a fee. It is a sum of money staked as a reward to incentivize a behavior which may or may not happen.
That's called a "bounty"
On BCH since next block inclusion is practically guaranteed with a small, predictable fee, we still have fees.
TLDR BTC has bounties, BCH still has fees