If anyone knows of a broker who will let you withdraw the proceeds (cash) of a short sale, I will buy the name of the broker off you. I'll also let you know why I would pay for this (although you may already know anyway, hah).
I spent a week researching this talking to fidelity, schwab, IBKR, and Robinhood, none would allow it.
Why would anyone let you do that? What's their incentive? I assume you're offering something as security for that money (shares?) but why would people complicate an already risky proposition further or go into the money lending business that they're not in?
I asked an adjacent question to a broker friend who flatly replied: "Not interested in being served a Wells Notice."
Which more or less answered the question for me, even if he was being a bit hyperbolic.