I have been using Binance Exchange peer-to-peer feature for a very long time now and there's no need for anyone to know the location for the zip code of seller, all you have to do is provide your bank details where you will receive your payment and Binance will release your crypto asset to the buyer after you have confirmed that you received the fund.
Before using Binance for "fake" p2p, they must have farmed your data and personal information, this data can be requested by the government, Binance can be breached and there will be a data leak, this way you personal data will be selling in the dark web; so Binance is not a better option, centralized exchanges are data farms and isn't recommended for people that want to trade and still have their privacy.
But, My question is if one thing or another happens in the transaction process, are we ready?
In p2p exchanges there is also a method of resolving disputes, everything is open and the parties will be involved in it. E.G in Bisq all the funds in the trade are kept in a 2-of-2 multi-sig wallet controlled by trading peers, and there is also a time-locked transaction set, this will send all the funds to another address that is controlled by Bisq, but this will happen many days after, if disputes isn't still resolved. So it is either trading peers reach a resolution, or the matter moves over to a mediator for settlement, if a middle ground cannot be reached, the arbitrator would have the final say, but that is when the time-locked transaction has been published and the funds is now with Bisq.