My sweep account on my brokerage is regulated by the SEC. I can’t trade it. Some of the challenger banks are using sweep accounts instead of standard deposit accounts. Just look at the ones with a broker dealer license.
Sweep accounts are not regulated by the SEC, they're regulated by the FDIC and other bank-related regulatory bodies. They may be offered by SEC regulated brokerages, but that doesn't mean that the accounts themselves are regulated by the SEC.
FDIC insured if the money is stored at a bank. Those are called brokered accounts. Not all sweep accounts use them and use money market funds or other securities. Also brokered accounts are fungible money can and does get transferred around behind the scenes. Some broker dealers will use the cash for overnight lending for income.