Usually the patient copays are substantially higher for brand drugs than generic ones. And the insurance company paying obviously isn't free money either, it's from premiums that people pay every month (and/or taxes). At least in the US, people often don't get medical care because of the expense, so anything that inflates the cost further can be expected to cause real negative health outcomes by pricing more people out.
I agree it would be better to not change even minor things if a drug is working. But I think that problem would be better solved by (as a condition of drug approval) requiring companies to disclose coloring agents, binders etc to generics makers once the patent expires, so they can make the exact same drug that was used in the initial clinical studies, rather than overpaying for drugs by 5-7x.