If they're regulated, next time they drag someone off a plane, they'll say "We were just following the handbook and were in accordance with federal regulations. Take it up with the FAA"
So no, no need to regulate the industry.
Also, the body you want to regulate them (the government) routinely does much, much worse to people.
I agree; hard to see precisely how more government intervention should have been expected to fix this.
One of the more promising candidates for the cause of such great expense for various services and projects in the US versus other (generally more-regulation-heavy and more-worker-friendly) OECD states, as recently discussed on here (following a Slate Star Codex post on the topic) is the risk/expense of relying so heavily on contracts and lawsuits to sort out this kind of stuff on a case-by-case basis rather than simply stating that things will be a certain way through regulation, removing (or at least greatly reducing) the uncertainty.
There's more volatility in the stock to be sure, but I wouldn't call this "paying the price for this mistake" according to public perception just yet. I don't know airlines well enough, but if I were going to take a position, it'd be long. The initial dip in the stock price tapered off, and the current price in pre-market trading has reached parity with 4/7 despite the relative increase in volatility.
Aside from market perception, I don't think UAL is going to lose much in sales (I'd love to be proven wrong though!). Airlines do not seem to really need to compete or differentiate themselves in customer service to be profitable.
These controversies have an impact on the stock price that is like the "villain of the week" impact on a show's overall plot - it's entertaining this week, but next week no one is going to care.