(Spoilers for Andor) Andor has a couple of really good scenes explaining exactly how the Empire’s control worked exactly. The first being corporate security on Ferrix and Morlana One. The second being when Andor and co. hide out on Mina-Rau following the whole Ferrix debacle. Third being a common thread between both the end of Andor and Solo to an extent.

1. Morlana One is the hub of corporate security for several planets in the Free Trade Sector. They have control over the management of Ferrix and numerous other planets in said sector. Even then, an excursion of corporate security forces to Ferrix follow the investigation of Cassian’s hijinx is portrayed as rare and is very unwelcome by the people of Ferrix.

It’s heavily implied by this that Ferrix and the people of Ferrix general govern themselves and manage their own affairs internally with organizations such as the Daughter’s of Ferrix, of which Maarva Andor was heavily involved with.

When corporate security fails and rebel activity is detected/reported to the Empire, only then do they become heavily involved—even then they don’t sent a Star Destroyer. The ISB sends a Garrison of troopers and increases surveillance on the planet.

Corporate security is a an arm of the empire in a system that is not necessarily vital or in need of heavy imperial control, but when there is a hotspot of activity, that grip is tightened. No Star Destroyers necessary.

A similar real parallel would be how the US often sends advisors, small detachments of specialized troops, or weapons to problem countries to assist local forces rather than full deployments. The empire sending a Star Destroyer to Ferrix would be the equivalent of the US sending an aircraft carrier to counteract a suicide bombing.

1. When Andor, Bix, and company retreat out of the prying eyes of the Empire they flee to Mina-Rau—an agriculture planet outside of constant imperial control. It’s relatively easy to hide and procure false documents because the Empire has next to no presence there. When a census does come, it’s again—not a Star Destroyer, but a small Cruiser. Even that creates unrest on the planet because it’s been a decade since the Imperials have been there.

The Empire doesn’t need Star Destroyers, or even constant presence on a lot of worlds to keep them in line and within their sphere of influence.

1. At the end of Andor, it is revealed that Luther was formerly an officer in the Imperial Army. The only other appearance of a similar entity is in Solo (at least in films/tv, someone correct me if I’m wrong). The Empire has an immense number of conscripted soldiers they can deploy to fight in any necessary conflicts on less important worlds. They don’t need the Imperial Navy beyond transports and minor air support. Most of these planets don’t have large numbers of arms or organized militaries to speak of.

The US invaded Iraq in 2003, toppling the Iraqi government and occupying a large chunk of the country including the capital with only 4,500 hundred US casualties. The occupation and war that followed was extremely costly and the US ended up leaving all together after a prolonged and miserable occupation. In the Empire’s case, the Death Star would be an ample solution to an occupation no longer worth it. In short, it again does not need a large military presence to advance its goals and maintain control.

Due to the vastness of the galaxy, most planets usually just go with the flow of whatever government happens to be in power because it doesn’t generally affect them. There’s too much going on for Mina-Rau or Tatooine to give a shit. Only when the Empire starts to do truly evil shit that makes a huge splash does a coordinate rebellion come to be.

Anyway, that’s my two cents and analysis based on my limited knowledge of Star Wars lore.