Most gambling sites don't have that feature. And it might become a problem if users can freely set their preferred fees then in the end it will get stuck.
In this case, players are responsible for their own withdrawal.
So if players choose to set a low fee and get it stuck then it is their own fault.
Actually there are some sites with this feature and I do not see any significant issues with this kind of feature.
Betnomi does not charge the user any fees for withdrawals as per their FAQ.
To save fees, only choose coins with less transaction fees. Betnomi has a great number of supported coins with less transaction fees.
There was a problem previously where betnomi sent a withdrawal with too low fee and withdrawal stuck for 2 weeks IIRC.
It was doge withdrawal unfortunately which should be a better choice for players to get the withdrawal confirmed faster and betnomi do not need to pay big fee.
If betnomi prefer to have "no withdrawal fee", they need to assure players that they will send all withdrawals with appropriate fee so it wont get stuck.