At Stripe, when your RSU vest, you still don't have the ability to buy the shares. Instead you have to wait for a liquidity event, or for 7 years to pass (making the shares worthless).
Publicly traded stock gets deposited in your brokerage account because your employer is publicly traded. Private companies offering double trigger RSUs that don't turn into shares or cash until a liquidity event (I.e. an IPO). At that point (plus a lockup period, maybe, depending on how the company goes public) the shares, minus withholding, will get deposited into a brokerage account and be available to sell.