Like that’s the ONLY reason someone would kill House. 
I can just see it. House’s dead body is found by the pair of bisexual identical twin hookers (plus pony) he’s hired for the weekend; he’s been strangled, shot, smothered, suffocated, and bludgeoned. There’s a police investigation. they don’t let Tritter lead if, of course, but he’s called in to consult. Asked who might be a good suspect, Tritter scribbles down the names Cuddy, Lisa, Wilson, James, and House, Blythe. The other detectives ask him why these people are the prime suspects; Tritter responds that those are the only people who probably wouldn’t do it, and he’s not sure about the first two.