There would be some law enforcement issues as well. It's true that their volume has dropped due to the many competitors on the market. Especially centralised exchanges like Binance started p2p exchange. A large number of cryptocurrency users have been involved with centralised exchanges, and often we get all services in one place. Hence, individuals lose their interests in other p2p exchanges because of centralised exchanges.
LocalBitcoins were previously a p2p exchange, but they stopped being that when they made KYC mandatory, so saying they were a p2p exchange, and that competing with centralized exchanges is one of the reasons they collapsed is not true, rather what is true is that they turned into a kyc exchange and couldn't compete with other kyc exchanges, because their customers' had left them for other p2p exchanges.
LE cannot also be a reason why they shut down, LE loves kyc exchanges, they love services that can feed them with customers' data, so there was no way they were going to have problems with LE when they comply with their laws.