I think it's okay to log in as long as you have optimum security in place, like 2FA. Anything you do on the exchange requires it, so you are safe even if you log in. That's just for me, though.
I'm an FTX and KYC-verified user, and here is what it looks like.

The only issue here is not security, but privacy.
You have now basically a KYC approved wallet.
If they share data (ftx and ledger, and they probably do), both have now your full balance and documents.
Additionally you are probably paying a bit higher than in FTX exchnage because you are a making a market order (swap). You are not setting a price , but buying from the order book