This is a great initiative to drive adoption of LSTs on different chains and L2s.
There are already protocols on those L2s that want to provide more value to LSDfi, and have already started doing it, despite a robust way to bridge these tokens. e.g. Cog Finance just launched on Scroll, which support different LSTs in isolated lending and borrowing. It also uses my xF33d contract to send the exchange rate from other chains (in this case from Arbitrum → Scroll) via LayerZero to Scroll, as a safe alternative for non-chainlink evm network.
Given we have this, it would enable those protocols to grow, further growing LSDfi and give more usage to the LST itself.
It will also benefit a lot of cross chain swap and bridge protocols, as they could give their users a better rate now, when wstETH is bridged. So, more people would want to bridge it.
The cost of arbitrage would also decrease, as people could seamlessly move across various L2s with fraction of cost. No need to go via mainnet 
It is a much needed for the Lido DAO to catch upto new age LSTs which already have it.