Here in the USA it's easy to get the idea, from various pop media, that there's vast stretches of 'Outback' that are essentially lawless!
Similar distance issues as the US. Far less "government is EEEVIL" attitude. Most public employees in small country towns (like police, teachers, social welfare, hospital, etc) are employed by state government, as opposed to local government (which is I understand the case in the US), so there is much greater sense of being plugged into a well-resourced organisation with more even standards of quality. "Corrupt local cops/town council" trope doesn't really work when a large proportion of public servants work in isolated areas for only a few years before being transferred (especially if going into leadership positions).
At least, that was my experience when I worked in a teeny-tiny town in the Outback (Brewarrina) for 12 months. And my Dad was a district relieving teacher employed by Education Queensland, so we saw our fair share of single-teacher schools across rural Queensland too.
Can't comment of "distant empires" in American history.
Roman Empire took about 4 weeks to travel from the Metropole to the periphery. British Empire, during the mid-1800's, took from 10-12 weeks to get from London to Sydney (and longer yet to get to outlying areas. By definition, there would have been a fair amount of local autonomy regardless of the legality of things.
French law was meant to set the standard in Saint-Domingue in the late 1700's. However, it was not unknown for the local Governor to not _publish_ changes in French law ...
'Single-teacher' schools are still present in the US but are increasingly rare.
Schools with 'combo-grades', (I, myself, was in a '6-7' way-back-when & I came across a couple '1-3's about 20 years ago), are more common.
In the OTU, what with 'planetary charters' & all, I envisioned most of the nobility as akin to the UK 'lords' in the 18th-19th centuries, with, of course, some notable exceptions.
However, with the later establishment in TU literature of a somewhat 'formal' titular hierarchy it would seem that the entire 3I is carved up into various titular 'territories'.
Still, I would think in most case, you would see something like this;
"Yeah, yeah, OK, your lordship <heavy sarcasm> you may be the 'Count of ?????' but I am the elected head of this planet's gov & our Imperial Charter means that your writ only applies to your private estates!
If there really are 'local' moots, I see them as more like a local 'House of Lords' as I can't see them doing a whole lot more than the Imperial Moot does. I see subsector & sector govs with assemblies of some sort representing local govs but not restricted to Imp Nobility. I also don't think the Domains would've had time to be become as dominant as Illelish/Dulinor were presented as at the time of the Rebellion.
Heck, the IN didn't even include the Domain as a command level anymore by the time of the 5FW.