They'd compete the same way they always do... by providing something (guarantee, etc.) the deregulated companies can't. It'll cost more to be "regulated," but that cost is passed onto the consumer. If the consumer puts X guarantee about price, boom, competing. If the consumer doesn't then that means X guarantee isn't necessary and it's time to stop being "regulated" before they go out of business.

Then again, even if regulation doesn't help at all, it's still a name; something familiar; something proven. Why do people by OEM hardware packaged by a familiar company at twice the cost when they could just buy it OEM?

And, as you can see with United and American, the other thing they always do is fail. The answer to "how do you compete when you have a huge regulatory burden that a competitor providing the same value doesn't" is, you don't. And again, that was just price and route deregulation. Southwestern still has to comply with the FAA.

There's no regulation a PickupPal driver needs to comply with. You can't start a nail salon without jumping through more hoops than a cab driver would to sign up for this. How do you even tax it?

I'm not sure what you're arguing here. I don't disagree that if two companies are providing the same value and one has no regulatory burden, that company will succeed while the other will fail. That in no way proves that deregulation is bad, it merely proves that regulation was, apparently, unnecessary in that instance.

I just don't see the debate here. If you provide X under regulation Y and I merely provide X, if the average consumer doesn't care about regulation Y then you will fail because I can afford to provide X cheaper than you. If the average consumer only feels warm and fuzzy with regulation Y, I will fail because we are obviously not providing the same (perceived) value.

All your Southwestern analogy proves is that price and route regulation is really stupid and wasteful.