It used to be allowed, that's how we got the big three, and SWA did some M&A along the way.

The current market isn't really "rigged" it's just by it's nature very difficult to break into due to both the obvious factor of economy of scale but even more so the fact that most customers prefer a large network.

Small newtork only works for annual vacation travellers, or people who happen to have a specific reason (business, elderly parent, etc) to regularly travel between two airports which don't have regular or direct service by the big airlines.

Otherwise network access, loyalty programs, and reliability win out.

Now did Lina K get paid off by the legacies to torpedo NK? That would be "rigged" but there's no actual evidence of that that I'm aware of.