Exchanges will always identify IP because they are very strict with it, as some nations have restrictions on crypto, so that they would be careful not to have anything to do with those nation, but when somebody uses a vpn or proxy that looks suspicious or IP from a restricted nation, there is every tendency that the account would get suspended or freezed and most times not every newbie have that knowledge as some too do not read ToS before they get registered with exchange so it is not advisable to keep assets with exchange and I align with your opinion that OP should use exchange wallet because nobody would require ID for transaction on a personal wallet.
Yes that is right that exchanges are very strict about tracking IP addresses because of international laws designed to avoid money laundering. Using VPN can get your account frozen as exchange security system can not tell difference between you and hacker trying to steal your funds. Due to this it is much better idea to use personal wallet where you have complete control over your assets and d not need to worry about your account issue frozen or having to provide ID for KYC. With this you are in charge and avoids risks that come with relying on third party.
Using your personal wallet is much safe and secured compared to exchange which can not even guarantee their own safety not to talk of their customers safety. Lately their have been lots of hack from exchange and they could not detect their lapses early enough to stop it so how will they tell us our funds are safe with them when they too can not be trusted with our assets even after taking our details and information.
As for the IP matter, it is wise not to use VPN because that would actually get the exchange confused and possibly hey you account blocked or freezed because of irregular IP which would warrant your attention before they unlock it to be sure you are the one truly accessing your account from the strange IP.