Why is Repyblic, the actual carrier, being let off the hook for everything which transpired?

Perhaps people from New Jersey would try another airport in NYC if it wasn't so difficult to get across the George Washington Bridge. 😜😳

United has deeper pockets.

And, boom goes the dynamite

Since this occurred in ORD, customer service agents are UAL, Supervisors are UAL, boarding policies are UAL, Operations are UAL. Everyone along the decision making chain is UAL.
Who UAL chose to fly the tin can has nothing to do with this.

Interesting point. The ticket says "United" but it's odd for the CEO to essentially say that, assuming responsibility for contracted flying. Smisek testified to Congress that not now not ever no how no way the Colgan crash was Continental's fault, even though the victim's families tried to tie it to Continental for years, and were making progress. But each settled until the last holdout was a relative (father?) of someone killed in the house the plane crashed into whose case was I think fell under a legal maneuver in the merger and had an ordered or forced settlement. He hadn't settled because all he wanted was for Continental to be held legally responsible for the accident because they sold the ticket.

So, God forbid another Colgan occurs, it will be hard to take the position Smisek did that litigation stops at our door. And painful as it is, I think that would be a good thing because if the legacy is legally responsible for the contracted carrier then it makes less sense to even have a contracted carrier since you have to control the quality of product yourself from maintenance to customer service to pilot qualifications and safety. I suspect, but don't know, that it's likely tied to the cost of accident insurance. If a court declares at any point that the legacy is legally responsible for punitive damages of a contracted carrier then the cost of that insurance may be so great that it would make more sense to just own the contracted carrier to control the product.

I think the difference between Colgan incident and this incident on the Republic AC, is the door was closed and aircraft was being operated by Colgan, under their certificate issued by FAA. The accident was attibuted to Colgan's operational and training pricedures.

This case, not so; the entire process was under the control of UAL's CSA personnel right up to the customer being dragged off the plane. The only saving grace for UAL might be to argue they called the Chicago airport police personnel to do their job, and they had an expectation that it would be handled professionally by the same.

But I think it would be grasping for straws to blame this in any way on Republic or their crew operating that aircraft.

Good point. But once it gets into the media and congress, logic and facts are overtaken by optics and perception. But you're right, it may be a stretch to compare the two. But one can hope that the company that sells the ticket on their website is fully responsible for that ticket anywhere it's used.

Lawyer right now: "what was the flight crew doing?"

Were the pilots even there?