The way I see it, this situation is like any national border on earth can be crossed , anybody could sneak onto a planet. The Imperium only administrates a few select worlds themselves, everywhere else the imperium is the mainworld starport or starports, and access to interstellar travel is what the visa is good for, it allows you to access the starport and take passage on imperial registry ships. It's not for entry into Regina, it's for exit from Regina. Unregistered ships are subject to interception and boarding and or sieziure, and registered ships are the only ships allowed at the starport, with exceptions for visiting foreign naval vessels showing the flag, and interface lines of course.
The Imperium controlls the space between planets, so you have to turn it around to the imperial visa is how you leave the planet. The planet will have offices at the starport to allow entry controls on whom they let in, but the Imperial consolate offices controls who is allowed into the starport and allowed access to the imperium at large. Therefore the consolate offices would be strictly sized according to the demand level of that world's citizens for interstellar travel.
The Imperium controlls the space between planets, so you have to turn it around to the imperial visa is how you leave the planet. The planet will have offices at the starport to allow entry controls on whom they let in, but the Imperial consolate offices controls who is allowed into the starport and allowed access to the imperium at large. Therefore the consolate offices would be strictly sized according to the demand level of that world's citizens for interstellar travel.