Why doesn't Robinhood just close the positions?

I'm pretty sure you could try something similar at any broker (write options, use the premium to buy on margin, rinse repeat), not all will block the trades but they do an account exposure/margin assessment periodically (hourly? daily?) and then take action.

For example a full service broker might call you and tell you to get within limits (a "margin call"). Low cost brokers like IB will just close all your positions regardless of loss.