I think converting Bitcoin or crypto currency to fiat currency always involves some privacy violation.
I think I would agree with you in this particular aspect. When making payment, definitely one would make payment with buyer and seller account names revealed which one can easily trace them from. P2P can only be okay when it comes to the buyer and seller location from different places for which they have no contact but their names revealed which means their identity been revealed. This alone tells that p2p have some privacy violation too.
I am not seeing any problem with the P2P service Binance providing even though you can not see your buyers or sellers name or identity. If the seller doesn't want to release the funds after you make the payments then appeal to the exchange with proof they will take a look at it and if your data is correct they will hand over the funds to you not to the seller. So I think it's simple and secure to use this kind of service on an exchange like binance.
That's the good thing with binance p2p, if you have complaints, you can easily file as they have buttons to report your tx.
And if you happen to use their p2p services, it means, you agree with the terms and conditions attached to it.
This is why if you have privacy issues, then, don't use this type of trading. However, it is hard to find trustworthy p2p services these days.
You can't avoid such privacy concern because it is hard to send funds to someone if you don't know their name and acct number, if you opt to send it to your bank account for instance.
One thing about Binance P2P service is you can't get scammed, I have been scammed using a p2p website before and the customer services don't helps instead they supported the criminal that I was paid with, since that day I was scared to use any P2P services, until I started using Binance exchange, the way they handle transactions is very well planned.
If you don't worry about privacy I don't think there is another exchange that's better than binance exchange peer to peer service, I have used Luno and Kucoin in the past too but the feel of security is not like Binance, it's true that Binance is centralized, but securing my transaction is what they do really well.
About what OP is talking about, not all those who asked for phone numbers plan to take advantage of you, they want your number to alert you to release fund when you get your money credited to your account, have none of you on a single transaction for over 24hours? Especially when there is a network issue with your banks, so I don't really think it's wrong, but this is a matter of choice, you are free to say no to submitting your numbers.