It's more complicated than that of course, but your point is not unreasonable.
At the same time, The Imperium is embodied in nobility who run the subsector capitals. Norris' allegiance is to the Emperor. Regina will have support from an imperial battle group, for at least as long as there is a credible threat to the Imperium. This is on the one hand very useful, and on the other manifests the responsibility and allegiance of Regina, and Norris, to the Emperor.
Still, colonial elements are generally local, and not at the Imperial tech levels, although they are quite often made up of older fleet elements which have been farmed off.
There are many different kinds of colonial forces.
Forces on loan from the Imperial Navy.
Forces sold off to worlds from the navy. Older ships but still useful.
Mixed forces for patrol, survey, escort, defense, and projection. Various mixes of these, and even some missing.
This varies based on a world's situation and needs.