To me it was character development. His whole persona is this independent persona - his genius puts him above normal people, rules, and his team is merely there to execute his ideas and bounce ideas off of (like his ball).
Despite all of that, he has crippling pain and a painkiller addiction that he’s utterly dependent on. It brings him back down to earth.
Closer to the end of the series, he basically loses his mind and is destructive to himself and others. An entire plot line was House hallucinating that he had quit and recovered from withdrawals (among other imagined or altered events) only for it to be revealed that he was using more than ever.
So, he canonically has more problems with drugs than social disapproval.
House was at least in part based on Sherlock Holmes who infamously had his 7% Cocaine solution. It's not entirely unreasonable to think the writers of House would update that to be pills.
How would "hey we can include your product in our TV show" be a "vast conspiracy"? It's done all the time, with no one hiding any aspect of the business.
I hadn’t heard this point of view before but it doesn’t seem too unlikely. The homage to Holmes is an effective way to hide it. That’s some good plausible deniability.