"Integrated cash management" (a debit card, etc) is abundantly available from discount brokerages, and is systemically important to their businesses. Fidelity legally can't call it a checking account so they call it a Cash Management Account; brokerages that own banks (Schwab, etc) just call it checking.
You did not answer my question. As far as I can see, the Fidelity CMA allows you to withdraw cash using their debit card, but I see no way to deposit cash. Nor does it provide features like cashier's check.