The stuff banks invest in isn't really "low risk", they invest in things like long-term loans that have a non-negligible risk of default. In order to be properly safe, a stablecoin would need to invest in much lower risk investments like money market funds and high quality commercial paper, which tends to have very low returns. The stablecoin would also need to have proper custodial arrangements in place which would cost money. Companies like PayPal do something similar as a way to avoid holding many millions in a bank account (which, as well as being subject to the credit risk of the bank, could attract significant fees and possibly negative interest). They almost certainly don't make significant profit from the practice.
What you are describing does happen, but it's not banks that do it, it's money market funds.
What you are describing does happen, but it's not banks that do it, it's money market funds.