I do P2P trading on Binance almost every day. But I never needed a VASP license to do P2P trading on Binance. Only the Binance account has to be verified. To verify my Binance account, I needed my phone number and national ID card and had to do face verification. P2P trading on Binance is easy and risk-free. So I suggest you do P2P trading through Binance.
His problem is not the platform where he can make P2P trades, but it's about his bank that is against cryptocurrencies or P2P trading and they aren't allowing him to do that which I think is a problem in most countries these days, and not only Estonia.
If I am completely honest, P2P trading has a lot of risks these days, and those risks aren't about you getting scammed out of your crypto, but it's about getting your accounts blocked and funds confiscated either by the management of the service you are using or the authorities involved in monitoring financial transactions. A lot of transactions are marked as fraudulent transactions and if you receive such an affected transaction, your account is gone for good, as you mentioned yourself, banks and other financial institutions in most countries are against cryptocurrencies, so they won't help you or get you out of trouble if you tell them the truth, so it becomes a situation where you are completely stuck with no solutions.
The people that you see on P2P platforms making trades are playing with all these risks at all times, some of them have mastered the art and they know how they can safeguard themselves from all these problems, some know the risks and are still doing it for the profits they are getting.