He might have bounced off the guard rail or be stuck in it just the same with extra material surrounding him and catching fire.
There have been also at least two cases I remember of race cars becoming airborne after touching wheels and being able to continue the race. This usually happens when the field is packed after (re)starts. Deploying airbags in such cases would probably entail a chain reaction that might resemble corn being popped.
The last 10 years many of the F1 cars due to the rules had catastrophic loss of downforce if they got too near other cars. The drivers had to work around this by not following too closely. F1 rules changes recently have tried to reduce these kinds of issues.
But even this last season was somewhat ruined by one team figuring out to work within the current rules and not have the porpoising problems that wrecked the other teams cars because they'd lose their downforce. That made the racing less exciting. And the whole problem never had to exist if it wasn't for the rules.
But I don’t remember catastrophic loss of downforce as bad as this: https://youtu.be/e21ZjwZGjiQ
While the downforce loss was significant, it was predictable and could be easily avoided. The equivalent for ground effect, e.g. hitting a bump or curb mid-corner and lifting the skirt just far enough for the pressure seal to fail and your downforce to go from 100% to near 0% in an instant, is far more likely to lead to a catastrophic accident.
The air bags have been covered in other comments but similarly would probably reduce safety, not increase it. The cars are very much designed for safety, and to absorb impacts, which is why they are so much heavier than previous generations.
Just because all cars can get it easily doesn't mean F1 want it. Most often the quoted reason is to have a better spectator sport and to make it safer. I really doubt those reasons because you can still have a difficult and tight race while having all the modern safety features. For example why don't F1 cars have entire car air bags (ie air bags that envelop the entire car that deploy when the car goes airborne in a crash/rollover)? if it's too "heavy" just make a rule that all F1 cars need to have air bags so the playing field is even.
F1 cars should have self driving collision avoidance that can activate faster than human response times as well. that would be way safer for everyone involved.