But as I said everyone else in the show either just tolerates him or hates him.

And yet the show commands a large audience for years on end. So he's only "insufferable" in a comedic or dramatic sense. The character reactions are in relief and there to distinguish him as exemplary. They can't operate as objectively and brilliantly as House, so they burn out dealing with him for petty emotional reasons. Meanwhile, the viewers stick with him season after season because only the audience truly understands his tortured genius.

If someone thinks being tolerated at their job and at risk of falling out of grace as soon as you are no longer “good for the hospital” is inspirational than that is on them.

Its inspirational in the same way a child swearing that they're going to run away or die, and then everyone will be sorry that he's gone is inspirational inside their own heads. So, more self-pitying and self-aggrandizing. But yes, it absolutely fuels the delusions of grandeur that people idolizing the character have of themselves. "House is just like me! A brilliant man surrounded by people too stupid to realize how desperately they need us!"

There was a whole arc on him trying(and failing) to rehab from addiction too, was that inspirational?

It was more about the high drama interspersed with disability comedy than rehabbing him. And, in the end, he's back to work doing his genius thing. Turns out he didn't really need rehab after all, just like he always said.

I maintain that with regards to media literacy, if they can’t see how fickle and miserable his existence was then that is their fault.

I don't think the audience is blind to his misery. I think they sympathize with his misery because they are also miserable. And they conflate their misery with genius. "He's miserable because his intelligence has alienated his peers. So if I've alienated myself from my peers, then ipso facto... :very-intelligent: !"