If an exchange says there is no fee then you should not trust them because it is not a free service,they also need to spend money for running and promoting their webiste so there is nothing wrong in collecting the fee but you can try binance if you want to reduce fee.
But there are some exchanges who started with some discounted or zero trading fees. Especially some exchanges with promo, like 1 week or more promo with no trading fees.
There are also exchanges that if they want to promote their exchanges, like for the first weeks/months they will not charge all traders on their platform for trading fees. And also there are some exchanges that you can get fewer fees when you have some holding of their coin, like Binance.