If the L1 ETH-USDC pool exists on L1, it automatically also exists on the booster rollup right? Unless I’m missing the point you’re trying to make here.
Because AMMs themselves are not easily scalable, I would see all the liquidity for a certain pool moving to one of the booster rollups. So the work for AMMs would be spread across the L2s organically based on where the most liquidity is for a specific trading pair, but in theory all the pools could be used on any of the booster rollups because the necessary smart contracts are there for all of them.
More complex parallelization methods would need to be done on an app by app level. For AMMs specifically there have been some efforts.