I bet if you asked 100 people about what kicked off the whole thing, 90% of them couldnt even tell you what other than Ned Stark being framed for being a traitor and 99% probably dont remember what, if anything, littlefinger had to do with it.
I think that LF is very much a dispensable character at this point. The only reason he stayed alive as long as he has, is because without him there is basically only 2 storylines left: Dany's invasion of Westeros and White Walkers. All the other houses are dead or irrelevant at this point: Martell, Tyrell, Frey, Tully, etc so there is not much in the way of intrigue, which is basically all of LF's storylines.