The issue of swapping assets between multiple blockchains can be a source of liquidity. It is crucial to lock and create, and burn, and release assets on different platforms since they are typically wrapped tokens used to transfer value across blockchains.
Each of these needs the pools of assets to constantly provide the needed liquidity to satisfy any request anytime. You can also navigate to https://rampdefi.com/ for cross-chain liquidity transfers.
In the scenario of bridged assets that have the same value, it presents an issue because liquidity providers are not incentivized by pricing strategies, but instead with interest-based rewards to be a way to compensate them for keeping their tokens in the lock for a period of time.
Therefore, ensuring the liquidity of several assets competing with liquidity providers is essential to the successful implementation of swapping strategies.
This means they will have to develop more complicated solutions that are difficult to generalize, which means that every pair of assets needs to be developed at the moment and each integration has specificities and peculiarities and, therefore, the bridging process can be supervised by no central authority.
Therefore, existing protocols have to adopt solutions to address the issue of liquidity and this is the most recent trend, mostly through the use of liquidity pools i.e. smart contracts that can lock, burn, or release tokens sync, so that the funds transferred from one blockchain remain locked and released on another.