Well I wouldn't say they don't screw each other over. CIVIL WAR and its aftermath was all about how FF/Avengers BS wrecked his life. When Tony and Cap fought each other and Reed built N-Zone Gulags and they cloned Thor, IM and the FF landed back on their feet while Peter lost his secret identity, had his Aunt shot, and lost his marriage.
Their comics before and after Civil War were more or less the same, but Spider-Man was literally divided into before/after. If you want you can also apply this to Secret Wars 1984 and 2015, where the first one led to Venom, and the second one imported Miles to 616.
So shared universe stuff tends to leave scars in Spider-Man's life/continuity in a way it doesn't for FF/Avengers. Not saying that it's not got positives (Miles) but generally that's how it goes.
Their great power, his responsibility.
With Spidey it's the other way around, the MU is a parasitic presence in his setting.it's for the best really, we wouldn't want Spidey to be a parasitic presence in the setting like Batman is at DC.