EigenLayer introduces the possibility of re-using ethereum consensus, and IMO the most interesting usecase for that would be building a decentralized two-way and security-optimal bridge between Bitcoin and Ethereum.
All bridges rely on the security of the two chains they connect and the security of the custodian^[1] used for bridging, since if the security of any of those 3 were to fail, it would be possible to drain the bridge (eg: if its possible to double-spend on any of the two chains an attacker can redeem the same coin multiple times).
However, if a significant amount of the total ETH staked were to be restaked securing this bridge, the custodian would be piggybacking on ethereum security, so those two become the same and thus you'd remove the custodian from your list of dependencies and you're left with only having to depend on the security of the two chains, which is the theoretical ceiling of security. In other words, you'd achieve the best possible security.
But not just that, you