Wilhuff Tarkin, the brilliant Galactic Imperial scholar, solider, statesman and victim of a rather obvious and controversial design flaw, was faced with the same problem in Alderaan that we now face with the Caliphate capital of Al Raqqa.
"...Alderaan was less likely a peaceful planet than a financial and intellectual hub of the rebellion, whose leaders, as we’ve seen, are totally untrustworthy negotiating partners — a hive of scum and villainy no less wretched than Mos Eisley, but on a planetary scale.
Invasion would initially be, of course, a cake walk. Salvaged military equipment and field expedient weapons platforms are simply no match for a hard core professional military, no matter how many Teddy Bears you bring.
However the problems of a long term occupation is a different matter entirely.
... invading Alderaan, removing its leaders and installing a pro-Empire regime...putting boots on the ground in this manner would likely have destabilized not only the planet but also the entire region, creating a breeding ground for religious terrorists and draining blood and treasure for decades. It’s not hard to imagine a Jedi State of the Alderaan System (JSAS, for short, though they’d likely prefer the simpler Jedi State (JS)) arising from the ashes of some ill-conceived invasion and occupation."
And there you are. The alternatives for 4GW in one package.
Occupation will be a long and involved process. One made somewhat easier if you have absolute control of the media to be certain but even that is hardly a guarantee. A string of pointless futile victories against an opponent who remains completely undeterred by those victories is utterly devastating for the occupier's morale. Even if that occupier is an effectively repressive dictatorship.
You are definitely talking about years of grinding attrition.
Integration into the Alderaanian culture will be difficult...because they are assholes and their women have stupid hairstyles. Storm troopers doing daily patrols will be taking casualties from Droid IEDs. The inevitable problems of recruiting during war time, will emerge. You might even have to go back to Clone Troopers and who wants more of those assheads around.
On top of that you are talking about a population of (wookiepedia check) 2 BILLION. You would be committing finite resource to a planet with an comparatively infinite population. Every single misstep by the troopers will create a recruiting drive among potential belligerents.
There is however an alternative.
The Hama model of insurgent suppression. Performed quickly it does give you instant results. And if it hadn't been for that stupid contractor error, (was it an error?...really? Honestly? I mean wake up sheeple!@!*). Tarkin would have been viewed as hard man who brought decades of peaceful stability to the galaxy. Look at the actual results of Hama Rules. Syria despite massively different ethnicities was the most stable non-country in the region for twenty years. The key to successful Hama implementation is speed. And lets' face it Alderaan was fast.
Of course there going to be immediate innocents in the vicinity who have no skin in the game. Babies in their mother's arms. Children flying kites. Tea shop owners who just want to sell you a cup of tea. They don't want any real part of this Jedi State. They just want quiet.
Here is the big thing about war.
The wrong people always die.
That is rule one.
When a civilization starts to do really well for itself, it always forgets rule one.
War becomes a game. An elaborate game. One with good guys and bad guys. A game that has strict, embellished and ornamented rules. Rules that must be obeyed at all costs.
Then along comes somebody that proves to you it's not. Oh no, it's not. War is not a game at all.
They are now attempting to victimize people who flatly refuse to accept that they have been victimized. It's like a con-man finally telling his mark, "no, look dumbass you got chumped. I chumped you. I took you to the fucking cleaners for everything you had and screwed your wife on top of it."
And then having his mark say, "no, you didn't. So lets not end this beautiful relationship because you seem to think you have wronged me in some way. Besides I'm sure it was all my fault. I probably deserved it."
To which comes the reply, "You are not wrong there."
*Think about it. An old psychic hippy samurai, those weird incestuous warlock twins and their drug smuggling boyfriend. Honestly how could this crew have destroyed the most advanced battle station in history without outside help. Work it out man!