its a central limit order book. a curve is a big pile of bids and asks at a continuous function. updating the curve per LP would require a price time priority queue for order fills.
One of the most powerful byproducts of the AMM is the LP token - it allows DeFi to be leveraged (in defi lingo, "composable") - can you think of how we can replicate such a construct in decentralized CLOB?
To begin, let's think about central MM. The MM is a service provider to the exchange. The LP token in this framework is a representation of share of service provided (work).