That's just the thing. The Moffs and other local warlords were, in many parts of the galaxy, the local governments
It would be more accurate to say the Moffs are the local representatives of the Empire rather than a "local government". Indeed they are a rather recent and parallel system to the Imperial/Galactic Senate which the Empire has been hollowing out and intended to discard in ANH relying on fear of the station to keep systems in line and the planetary governors to serve as the regulatory apparatus.
In most cases, considering the seeming unpopularity of the Empire, they were the "local government" only to the extent of the line of sight of the Stormtrooper/Imperial Army garrisoned there. And once they could no longer count on a Star Destroyer showing up likely not even that.
With worlds either being overthrown by popular rebellion now that the Empire has been shown to be both leaderless and far from invulnerable, possibly aided by both the Republic and the Hutts for their own purposes and advantages in terms of supplied weapons, or abandoned due to being untenable in a galactic version of the fall of Saigon or the US retreat from Afghanistan.
I'm imagining the Outer Rim falling apart in 4-5 ABY again drawing parallels to the fall of the USSR and how the abused outer territories very rapidly succeeded from the Union when the "Evil Empire" no longer had the will or capacity to force their submission.
It is these new independent governments, as proxies for Republic/Hutt interests and opportunistic despots and likely everything in between, which I referred to the ex-imperials joining in exchange for food, steady paychecks and protection from being punished for warcrimes
In contrast, the EU Empire actually had an estimated 25,000 Imperial Class Star Destroyers alone in its entire navy by the time of the Battle of Yavin, most of which were permanently stationed in the Core. This doesn't include smaller vessels, such as Vindicator cruisers among others, which were actually the workhorse of the Imperial Navy.
The numbers we attach to the Empire don't really matter. They could have 25 ISDs or 25,000. What we do know, even in ANH, they were already fears of the Rebellion gaining sympathy in the Senate and becoming a threat to Tagge's starfleet. That there is concern of keeping the systems in line and the solution is not through conventional military like stormtroopers or ISDs but the Deathstar wunderwaffen.
That, in canon, the Empire lacked the force projection to prevent or persuade the rather obvious military support the Rebellion was receiving especially by ROTJ.
And of course you don't control a planet with ISDs anymore than the US could control a country with airpower. To do that you have to get down into the nitty-gritty and enforce your will through bloody infantry potentially turning every world into a Vietnam Quagmire.
After Endor, that vast military more often than not just followed the closest, highest-ranking military officer, hence the EU Empire fracturing rather than imploding.
Well the events of the EU aren't being questioned only how realistic such a turn of events were. As far as it goes I don't disagree about the Empire fracturing, I think that's a very likely outcome, or that the military would revert to following the next chain of command. That is kind of why a chain of command exists.
The issues are that fracturing into warlords makes the Empire(s) weaker than the sum of their parts making it harder for them to react to either the singular in vision Republic or rebellious uprisings taking place across the breadth of their territory. That an Empire so weak the Core abandons it is an Empire likely too weak to hold on anywhere.
Hence why I reject the analogy between the Empire and the Soviet Union, and find Imperial China more fitting. The dynasty collapsed, central authority has failed, and the various armies and fleets of the empire now follow generals, admirals, and governors vying for power.
For me, I'd say of the two the USSR is the more apt comparison. Both are, essentially, post-industrial nations who treated the outer periphery of their territory poorly for the inner core's own gain to a dickish degree. That post-industrial armies are far more dependent upon the industry of their nation-state compared to pre-industrial ones making warlords while not impossible more limited than the ancient world hence why we typically see such arraignments more in places like Africa rather than as a peer opponent you can fight a direct war with.
An Imperial warlord would need to guard its manufacturing and refining industries, less a Republic commando team or the irate local populace blow it up, its mining and resource extraction processes to fuel the former and its agriculture and livestock, less farmers burn/slaughter it in protest much like the Ukrainians did against the Soviet. All while engaged with the Republic, other Imperial warlords or newly formed local polities. A failure on any front would ensure it could no longer function as a modern state.