Use an exchange wallet only for buying and selling Bitcoin. Do not store anything in an exchange. Even a hot wallet or a mobile phone wallet is better than an exchange. It least they won't ask you for an ID.
Also, I find that proxies will only increase the suspicion of cryptocurrency exchanges when you use their websites - as they can easily be identified by IP address.
Exactly storing your Bitcoin on exchange is risky because you do norlt actually own it but exchange does. With this your money can be hacked or other problems can occur and you lose your privacy since exchanges require ID. It is safer to use personal wallet which gives you complete control your assets.
And I agree using proxies or VPNs on crypto exchanges can raise red flag. These services can make your activity look suspicious to exchange security systems which can lead them to account freeze issue because they think it is used by someone else. So using exchange is best for simple buying and selling but for security and privacy it is good to use your own wallet and avoid proxies.