This sounds like a nice, generous thing to do, but basically it means that the drug company is bribing the customer to force their insurance company to spend more money on their behalf.

So, imagine that a drug costs $1000 and the customer's copay is $200. The drug company can give the customer a $200 coupon to recover their copay and then raise the price of the drug to $1200. They've basically shifted the price from the customer (who decides whether or not to get the drug and is probably very sensitive to price) to the insurer. They make the same profit, but can probably sell to a lot more customers because it's "free". While they're at it, they could raise the price to $1500 or $2000, and it's still free to the customer.

I think this is a corrupt practice and it's crazy that it's even legal, but it's just one small part of the complexity and perverse incentives of our health care system.

It doesn't work like that unless you're the only drug in class. If there are alternatives, then you'll get kicked off the formulary for a 20% price increase.

I don't hear a lot of complaints about medicare not covering important things (but I only have limited exposure to that), and I assume a US single payer system would essentially be Medicare for all. I do hear complaints about Medicare not paying providers enough, and a lack of available providers.

A rational method of rationing care seems preferable to the current byzantine methods. My (likely naive) hope would be that spending the same amount of money on healthcare, but with fewer parties involved would provide more and better healthcare. At least we haven't reached the point where the government encourages smoking to decrease long term healthcare costs.