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For DEX, most popular ones are using liquidity providers instead of order books while I believe we can build DEX on both models.

Then why is LP a better one?

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DEXes have long existed based on order books. Maybe the most famous one was (is) Etherdelta. It was kinda ok for years, but it was not very user-friendly and never gained enough users to make the trading liquid enough, except for many a few most popular pairs.

If there is no liquidity in a marketplace, the price of the tokens fluctuates too much and you may not even be able to trade.

Using AMM (or liquidity providers) mostly fixes the liquidity problem. Any user can create a trading pair and add liquidity for it.

Of course, AMM model still requires liquidity, but there is incentive for users to add liquidity, to gain liquidity rewards. That's why adoption is much faster and a lot of pairs have decent liquidity to make the price stable.

With order books, you basically had to hope someone wants to match your order. With AMM, you don't need to wait for someone to match your order and you can trade instantly.

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