Doesn't that rely on you being the actual owner of the shares? If your shares only exist in Robinhood's database, I don't think SIPC would apply.
EDIT: After some Googling it appears that SIPC does protect securities that weren't actually purchased due to fraud or mismanagement. IANAL so I don't know if that would apply to this specific situation, but they have protected other non-owners before like in the case of Bernie Madoff.
No, they are held in "street name" but the customer still owns them. You're not just a creditor of the broker. I've had a broker go bust, so I've been through the unwinding process.
A broker which just has pretend stock ownership as a book entry with the broker is called a "bucket shop".[1] A crime in most US states since the 1920s.
There may be regulatory technicalities that must be sorted out. But there isn't any reason this couldn't be handled in exactly the same way as street name shares are today. Voting rights would be interesting.
