I think it would be hard to make a decentralized swap exchange that runs between various chains.
We need some kind of bridge to connect between the chains, for example between Ethereum and Binance smart chain network.
And if there is one chain that have high transaction fee, then our cost to swap between chains will be high too.
Basically, there are many things to consider when we deal with different chains and networks.
This can be work, if the engineer is good enough most probably he can deliver the required network of the team and the project. You can operate DEX without having your own token but I believe this can only work at first because later on, you’ll realize the importance of having your own token and that could be your next big project, to introduce your own token.