Perhaps the decentralized exchanges where you can directly log in with your wallet will help solve this, as you have the control over your wallet and not the exchanges.
you still have to make on chain transactions and that will require paying on chain fees. so you won't be escaping that when using a decentralized exchange.
but there are solutions such as Lightning Network and the cross chain transactions called Atomic Swap which may take place on the second layer and because of that they can have nearly zero transaction fees. but I have not seen this in action so this is just a theory for the time being. hopefully it becomes a reality soon.