Lots of strategy games (e.g., Commander: The Great War) have a very simple system where areas that are not defended and do not contain significant cities/towns/VPs/etc. automatically surrender and are occupied, thus sparing the player the laborious task of having to occupy every hex/province/etc. yourself. HOI4 needs something like this.
If you like it can be limited to prevent exploits - the area must be surrounded for a significant enough time, it cannot be larger than a given size etc. etc.
None of which, it should be pointed out, is really all that historical. Historically MPs weren't CO-IN specialists, neither were cavalry - light infantry was just as good at CO-IN and arguably better in rough terrain.
The
important part which alot of you are missing or simply ignoring is,
that enemy countries will surrender everything (except oversea territory) to you if you capture enough of their Victory Points forcing them to surrender depending on their National Unity (which was bugged in WWW aswell because it is never supposed to be at 100% as daniel stated and is already fixed). You dont have to capture siberia for example, if you capture all the important soviet cities.
The only reason why Daniel basicly had to take everything was because the soviet national unity was bugged at 100%, which shouldnt be possible as stated above. If that is the case you need to controll 100% of the victory points of course, just ast with 50% national Unity controlling 50% etc.
HoI IV doesnt need a system to automaticly flip occupation of states, especially since all states have something of value in them, let it be cities, resources, airports or simply the state itself which is worth victory points on its own
and because it already has that exact system.
The main advantage of cavalry is obviously that it is very mobile and still really cheap. Thats the whole point, especially since you have no rebells to actively fight against. As for regular garrisons a cheap poorly equipped infantry division on low priority for supplies is of course the better choice, in europe for example. If you wanted you could even use 1 heavy tank brigade with an MP company attached with tiger tanks to supress the partisans.