Yeah, their leaders need to put a sock in it, though I will say we often haven’t helped, because every time it seems there’s a chance to rebuild some dialogue we tend to undercut ourselves. Then again, the hardliners in Tehran realize that constant crises may well be the only thing keeping them in power.
They do threaten Israel, at least verbally, pretty often, but I think the Israelis make a bit too big a deal out of it sometimes, as the current leadership in Israel also depends on having a boogieman like Iran around. The Israelis and Iranians have dealt with each other before, clandestinely, and much of the actual strife between them involves competition for influence in places like southern Lebanon, rather than existential threats.
The Saudis, though, are fully capable of funding and supporting whackjobs who would do something truly atrocious. The Iranians generally fund Shiite militias and the like.