I have never used LocalBitcoins.com for P2P but I knew that they have been here for so long. It’s the OG of the P2P crypto trading (but correct me if I am wrong). It’s just unfortunate that they have to close because of the declining number of traders in using their platform, so nothing is really permanent.
But there are still other P2P platforms from exchanges like Binance, KuCoin, OKX, ByBit, etc., that we can still use as of the moment.
There are many other platforms but believe me localbitcoin was something purely P2P platform. Currently, the platforms you mentioned above run a p2p program based on USDT and escrow funds are mostly centralized. On the other hand, LBTC had its escrow wallet but it was up to the user when to release the funds. You used to get money deposited from one bank to another bank account. The bitcoins used to be shared over secure wallet transfer from LBTC to LBTC address. It was way simpler, secure and most importantly it was truly anonymous.
In the case of other platforms, they are using stablecoins to do this job. It means you still need to sell out your USDT for the fiat and real money to arrive in your account.
In LBTC, payment was the bank to bank (with other options too) but that was justifiable OR it was pretty clear one could easily hide whether it was bitcoin money or not. It was cool platform.