They used to have the largest share of P2P trading volume, by a wide margin.

Then they made KYC a requirement. They are still the largest (by trade volume) in some countries, but they've shrunk dramatically in both trade volume as well as market share.

Paxful is now the largest, but some time after LocalBitcoins began requiring KYC, Paxful did the same thing.

OP specifically asked for KYC-free methods, so neither of those will work. There are a number of No-KYC (KYC-free) P2P trading platforms such as Bisq, Robosats⚡, HodlHodl, LocalCoinSwap, LocalCryptos, AgoraDesk, and a handful of others that are smaller or targeted to a specific language or country / region.