I would never trust a significant amount to USDT. It's not USD, there is no guarantee it's going to be worth anything tomorrow.
If I was a relatively active trader I couldn't afford to remove my USD from an exchange. It takes days to move around.
Assuming you're in the right area exchanges like Gemini have banking charters so your funds are protected by full bank insurance up to a certain amount even if they themselves go tits up. That's about as safe as it gets.
Actually I think storing fiat on exchange is safer than storing cryptos.
IMO hackers aim to stealing cryptos mainly.
In case of hack the stolen crypto is transafed out and as txs are ireversible there is no chance for exchnage to get it back. Contrary the fiat which can be tracked and/or canceled by authorities.
Moreover I believe any proper exchange dealing with fiats has to be somehow insured (for fiat losses ).
So to your question I would keep stored fiat rather than converting to USDT.
You're forgetting one rather large thing which is the most common form of hack is your account details being compromised. The hacker then uses your stored fiat to buy all the crypto they want and it's all gone forever.
The only time your fiat is safe in a hack is when the exchange itself is breached which is a much, much rarer occurrence.
You need to 2FA everything including email and make sure your 2FA isn't via mobile phone as that's far too easy to hijack.
Sure ... we can define a lot ways to hack ... hacking certain "wallet implementation" (more or less what I was talking about), hacking individual account ( in which case no matter what curency you stored .. it's all gone), hacked complete exchange security (also no matter at all .... it's gone as well).
I still consider my point valid because if you have a fiat stored in you are scared of 2 of those 3 things I mentioned ... thus it's safer.
Nevertheless non of us answered OPs question so I would sum it like this.
It's up to you to decide whether undergo the risk of losing it or sacrifice some time and fees for transferring your funds to safer place.