But, I rewatched the season ender of BBC's Sherlock tonight, the one where Moriarty kills himself and Sherlock fakes his own plunge from the roof of the building (HOW??) and got to thinking about that final episode of House. They DID give House a Sherlock Holmes death!
First, Greg House has no equal, his greatest enemy was only ever himself. In fact I think Wilson told him that explicitly more than once. So House was his own Moriarty.
House comes-to after having passed out shooting heroine with his patient in the upper story of an abandoned warehouse. This patient is a convenient cypher for House's struggle with himself and is conveniently dead. For whatever reason the building is on fire. House struggles with himself and decides he wants to live. Like falling over a waterfall, House falls through the floor to the ground floor below.
Wilson finds the burning warehouse just in time to see House's profile in the window, then the roof caves and House is buried in flaming timbers. Similar to how Watson sees Sherlock slam to the ground, head crushed, dead.
At House's service Wilson berates House for being an ass, like Watson tells Sherlock's gravestone how angry he is at him. House reveals to Wilson that he's still alive, having made it out of the back of the building. The body pulled from the burned-out building was his cypher patient.
And we know Sherlock is alive but don't know how he did it! Dammit! Anyway.
So that's how the show House had a proper Sherlock Holmes ending.
And I have got to quit being an idiot and get some sleep.