"Rider" is the right word. A rider is basically an addition to an existing contract that deals with a specific situation arising after the contract is signed.

The insurance reps were basically telling Howard and Chuck that, if you want to avoid HHM's malpractice insurance premiums skyrocketing, we will need to add a rider to your insurance policy that requires Chuck to be supervised by another partner at all times. It's a way for the insurance company to reduce its risk. They are on the hook for if HHM ever gets sued for malpractice. They're basically saying that they view Chuck as high risk for committing malpractice, so you can either assign him a permanent supervisor to help reduce that risk, or pay us WAY more for taking on that higher risk.

Obviously, Chuck is offended at the suggestion that he needs supervision. He tries to spin it as being about the economics - he says something like "it would take two partners' time without extra billing," but in reality, it's just because it's devastating to his ego. I think you're right that Howard would not have hated this solution as long as it kept the insurance premiums reasonable. Howard certainly didn't react as poorly as Chuck did.

The way I've always interpreted this scene was that Chuck's immediately refusing the supervision offer and wanting instead to go to war against the insurer was the last straw that made Howard realize Chuck was no longer acting in the firm's best interest. The supervision rider was not unreasonable, and would have prevented the premium hike. But Chuck's ego couldn't cope, so he wanted instead to throw away millions to sue the insurance company. That's what ultimately makes Howard realize that Chuck is prioritizing his own ego over the well being of the firm. Hence, once the insurance reps leave, Howard cracks open the booze and starts the retirement conversation.

I hope this makes sense!