IIRC, the old Legends continuity suggested Palpatine had the Empire intentionally designed so that should he be killed, it would collapse in short order without him. Basically an insurance policy to make sure that anyone who staged a coup, even a successful one, would regret it.Am I right in thinking though that the Emperor was supposedly holding a lot of Imperial forces together through the Force and sheer willpower? I thought I'd read that somewhere but maybe I imagined it!
As for the current Canon, we've seen in the ISB scenes on Andor an extension of what we saw in the Death Star briefing room scene in ANH that many of the Empire's authority figures are constantly at each other's throats. It's reasonable to conclude without a supreme authority figure like Palpatine or even Vader or Tarkin, that those pissing matches could degrade very quickly to infighting causing very real damage to the Imperial infrastructure.
IIRC, the New Republic didn't become aware of the First Order until six years prior to TFA.I guess there may still be a decade or so of relative peace before the rise of the First Order or is my understanding of the timeline way out of whack?