Correct me if i'm wrong but i think my friend once told to me that we can stake USDT to Binance, but if it is wrong then i missheard it. With USDT i think the only problem that we can face is security of the exchange or our own account. About price, maybe stable coin can help the price at least not dumped.
No doubt exchanges are under the top priority of hacks. If you want a safer option, there are custodial wallets which offer >8% APY on your USDT/ stablecoins.