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But that platform, or kind of, has been there for centuries. When you exchange fiat person to person, just like gold and silver coins a few centuries ago, that is a peer-to-peer exchange. How are they going to regulate it? Now, with the advent of cryptocurrencies and Internet, we are taking this exchange to the next level by removing distance from the equation completely. If you ask me, that's a natural course of events, and preventing or hindering it would be like trying to stop a freight train. Typically doesn't end well for those trying.
You may be confusing peer-to-peer with decentralisation, these 2 doesn't necessarily go in pairs. Binance is/will still be a central entity providing platform for P2P traders and as such, they could be forced to impose limits and comply with KYC requirements.
Even Localbitcoins seem to require ID verification above certain threshold:
https://news.bitcoin.com/significant-trade-volume-triggers-localbitcoins-kyc-requirement/I think this is still a 'grey area' in many jurisdictions, up until cryptos were introduced - such activities were simply not possible to do online.
Anyhow, the good news is, if there's ever too many restrictions on legal P2P exchanges, new 'underground' exchanges will quickly pop-up and take their place.