Decentralized exchange or not?

For me, decentralized exchange has always meant that any compatible token can be added with any amount of liquidity.

Nowadays, when cross-blockchain decentralized exchanges have been created, some require owners of the exchange to add tokens to the exchange, so same token in multiple blockchains can be treated as one.

This mean the person creating the individual liquidity pools doesn't have to pay the creation fee, so adding tokens is cheaper.

However, this allows the exchange owners to restrict possible tokens and token pairs depending on how much liquidity is provided by token creator or the community.