USDC is less 'frozen' than say USDT
Oh really? How do you explain that 1% of USDT supply is frozen while 1.7% of USDC supply is currently frozen?
(That makes even Wise and Revolut look safer! At least they give back your money after having them frozen...)
keep it in DAI
This is even worse than just holding USDC.
You can deposit your USDC on it, which gives you a new token called avUSDC (may vary depending on blockchain), which is a yield bearing token of the USDC you originally deposited and can be swapped back to USDC at any time. avUSDC cannot be locked/frozen, and the underlying USDC is pooled/lent out, so while it can be frozen, it makes no sense to freeze as it'd freeze the whole protocol.
Exactly, the whole protocol can be frozen. Coinbase wouldn't be interested in this at all, as this Protocol lending system is not a competitor for them. Oh wait, they are!