i wouldn't be so sure about that. only unlimited block size can keep the fees low. anything that has a cap will end up with a fee market eventually.
besides with BCH there are other problems too. for example what people sometimes forget is that BCH is the exact copy of bitcoin and the clients are the exact copy of bitcoin core and due to the incompetency of BCH developers they haven't been able to really create a client that works for that kind of block size. you would think that empty blocks and having such a huge cap wouldn't lead to fee competitions but you would be wrong. not to mention that miners don't even support the big block size after 2 years! and they will continue mining 1 MB blocks even if there were more transactions in the mempool. it is not noticeable because BCH block sizes currently are about 0.05-0.2 MB.

here is an interesting observation i had a while ago where a short term (1 hour) spam attack of transactions with 1 s/b fee forces users to start paying 2 s/b:
https://bitcointalk.org/index.php?topic=1776143.msg52337255#msg52337255