Swapping assets between multiple blockchains is a problem with liquidity. As these tokens are often used to transfer value between blockchains, it is important to lock, mint, burn, and release assets across multiple platforms. Each one of these requires pools of assets that provide sufficient liquidity to support any order.
Bridged assets with the same value present a challenge as liquidity providers can't be incentivized by pricing strategies, but they can get interest-like rewards to compensate them for keeping their tokens locked up for a while. If you want to get more information about cross-chain liquidity visit https://rampdefi.com/.
The key to efficient swapping strategies is to ensure the liquidity of all assets that are competing for liquidity providers' resources.
Although single and multi-chain aggregators have gained traction over the past 12 months, most seem to still be in their early stages. All of them are presented, directly or indirectly, as "liquidity protocol" and this seems the key issue. X-chain aggregators' strategy for bridging Blockchains presents a liquidity challenge that requires a solution.
This framework makes centralization a La Binance an "easy" solution, but it comes with the well-known problem that a single entity can control large amounts of assets. Trusted custodians who manage escrow accounts for their clients must rely upon trusted server operators block headers.
Decentralized custodians are not dependent on one point of failure at top levels. They can be trusted, however. This means they have to implement complex solutions that are difficult to generalize. Each pair of assets must be implemented at once, with each integration having its particularities and idiosyncrasies.
Existing protocols must find solutions to the liquidity problem. This is the main trend at the moment, which has been mainly implemented by liquidity pools (i.e. Smart contracts that lock, burn, and release tokens in Syncplicity.