I don't think any major retail broker is at risk of going under. What puts financial brokers out of business is proprietary trading or taking on some kind of securities risk outside the normal course of broker/custodian business.
Some were some not. Problem was that in many cases losses exceeded customer balances. Ibkr had such an issue when oil went negative (google it, a canadian guy lost almost 10 Million on <100k account). Ibkr had software glitch and miscalculated margin. They however did handle that well and just wrote off the loss (around 100M) and compensated. They probably would not have been able to collect much anyway.
Liquidity buffer is definitely important. The thesis of the OP is still wrong - profitability is not a sign that a broker is safe to put capital in. In fact, outsized profitability might be a red flag that the firm is selling icecream in the front and crack out the back. No financial company wants to be in the news for stealing Bill's family farm.
I think the have such high margins and then they do not invest enough in infrastructure thus such high pretax gains can be possible. You cannot compare them with Goldman by the way.