Not sure I can follow you there... bombarding a target to dust is really quick and cheap... especially with the kind of weapons we are talking about... fighting on the ground takes much much longer...
to bomb the whole of Japan back into stone age 1945 would "just" have needed days/weeks (if the US would have the number of bombs available which they did not - but in C# the attacker would have within his fleet)) but an invasion of the Japanese main islands would have resulted in fighting for a year minimum and would have been really expensive in terms of deaths and equipment...
bombarding - especially with nuclear missiles - should be really quick, really dirty and really devastating... but destroying a target from orbit should for sure be much more quickly than successfully invading it against opposition
That depends entirely on the nature of the target and the weapons.
For conventional weapons (and we can probably include orbital direct-fire weapons in this), engagements basically come in four varieties: Undirected counterforce bombardments, ground-directed fire support, terror bombing, and assassination.
Undirected counterforce bombardment against even minimally prepared ground forces is a way of punctuating your press releases and diplomatic communiques with explosions, not a serious military tool. The entire air campaign against Serbia during the wars of Yugoslav dissolution knocked out a mere handful of tanks, and this result is not atypical.
Ground-directed fire support is extremely effective at killing opposing forces, particularly vehicles and particularly on the defensive. The clearest demonstration of this recently was 2013-14 in Kobane, where the USAF chewed through a short brigade of Islamic State's only solid combat troops and all the expensive American hardware the Iraqi army left behind when it bugged out of Mosul. For offensive exploitation, however, you need infantry that is willing to take casualties, because you need someone moving forward to provide fire direction. This was one of the problems the IDF had in 2006, and a major reason Hezbollah humiliated their expeditionary force.
Terror bombing kills a lot of civilians and causes a great deal of expensive property damage, but not really enough to materially degrade the ability of the population to sustain a war effort. Even weeks of sustained carpet bombing with chemical and conventional weapons was insufficient to wipe out Fallujah, Mosul, or Raqqah, which still had to be taken through ground assault. (This is not a USAF problem either; the Russian air force could not bomb Grozny or East Aleppo into submission either, despite pounding most of the buildings to rubble.) Similarly, studies of the carpet bombing campaigns of the second world war tend to conclude that they cost more to conduct than it did to repair the damage done by them.
Finally, assassination is perfectly feasible, but depends heavily on the quality of one's targeting intelligence. We've seen both extremely precise targeting of militia leaders, and the occasional wedding or funeral getting blown up. Either way, it's not really in scope for Aurora - it doesn't have a sufficiently sophisticated political model to properly simulate (counter-)insurgency warfare.
Once you break out the nuclear warheads, the feasibility of undirected counterforce bombardment and terror bombing increases, but it's still not a simple exercise to glass a major planetary population. Assuming one point of missile warhead strength equals 10 kt (making Little Boy somewhere between 1.5 and 2 points), and a typical early to mid game warhead is 15 points, you'd need ten to fifteen of those to blanket a mid-sized city like Berlin with blasts that will reliably knock over sturdily constructed buildings. If we assume that one warhead point is about 100 kt, you'll still need six impacts (though if you're satisfied with killing the people and leaving about half the buildings standing, you can make do with three). And Berlin is not even in the top 100 cities of the world.
To comprehensively demolish the industry of a homeworld, you'd need somewhere between one and ten thousand strength 15 impacts, depending on your assumptions about how warhead strength translates, and the distribution of industry across the population. This can be done, but it's not a trivial expenditure of ordnance for an early- to mid-game empire. And to wipe out the population, including dispersed rural communities, you would need far more (though the collapse of industrial society resulting from tearing out the major industrial centers may well take care of that for you).
And counterforce bombardment remains non-trivial, particularly against dispersed or well prepared infantry and static units. You'll often have to literally dig them out of fortified positions, which means putting multiple impacts on top of them with fairly high precision. It can be done, but again, not a trivial exercise.
The rules outlined upthread seem to capture these realities reasonably well. If you're willing to simply pave over the planet, you can with reasonable ease nuke it hard enough that it becomes worthless to the defender (which means any ground forces holding it are simply eating maintenance while providing no value in return). But if you want to eliminate a troop concentration, then you need to invest the planet with at least some ground forces to provide fire direction. And if you want to take the planet mostly intact, you need to do it on the ground, with relatively light troops and minimal orbital fire support.
