The Inquisition was a paper tiger. Some, if not all, of its martial might was either borrowed from Orlais and Ferelden or had family in those nations. How many folks do you think would stick around to support an armed insurrection by an organization whose purpose was ended in the face of having to fight their friends and families?
Skyhold is absurdly vulnerable to seige, because you don't even have to beseige the castle itself, you just need to close the passes leading to it. It's a minimal cost solution to an organization that thinks far too highly of itself. The three other taken keeps would be considerably more difficult to take back, though hardly impossible.
Orzammar under Bhelen might momentarily consider aiding the Inquisition, then his brain would start working again and he'd remember that Orzammar is entirely dependent on trade with Orlais in order not to starve to death, as illustrated quite clearly by the dwarven delegation at the ball.
Any other potential allies would be too far away to help, assuming they cared or didn't have issues of their own to deal with. Nevarran tensions with Tevinter keep them from getting adventurous, Tevinter has to worry about the Qunari and each other, Starkhaven either isn't friendly with the Inquisition or is tied up helping restore Kirkwall, and so on and so forth.
Not even the Chantry, with all its political power, could do more than delay the inevitable. The intelligent members of the Inquisition know it, which is why they bothered to show up to the Council at all. The Inquisition was never in a position where they had a choice to ignore the dictates of Orlais and Ferelden. At their best, the worst they could have done was make it painful for those nations to enforce their will, which any true organiztion with the 'good of Thedas' in mind would have avoided at all cost.
I think Orlais and Ferelden were the paper tigers. Vivienne as Divine even states this as fact. The only time the Inquisition needed those soldiers was when they took down Corypheus' forces in the Arbor Wilds, and even then the Inquisition did most of the legwork. As for the Inquisition soldiers being from Ferelden or Orlais, sure they were, but what does that matter if their countries attack the Inquisition? Remember, Ferelden wars with itself all the time. The banns start feuds over many frivolous things, even an apple tree one time. Orlais is ruled by rich, pompous elites who bring ruin to each other for fun. How many Inquisition soldiers would prefer that over the Inquisitor who saved the world from a vile evil and terrible cataclysm? And how many of these lords would turn down a deal from the Inquisition to betray their own ruler(s) in exchange for more land? Their friends are the other Inquisition soldiers, and their families would most likely either not fight the Inquisition, or probably join them.
There are too many passages to block, and the terrain favors the Inquisition. Ferelden would not consider it a minimal cost once their patrols start getting curb stomped by mages and soldiers working together.
And then Bhelen would remember that the Inquisition knows the truth about the titans, and he would seek out trade with the Free Marches instead. The Inquisition's good friend and Viscount Varric Tethras could help with that.
Frostback Basin, the Dales, Kirkwall, and possibly Ostwick if the Inquisitor is a Trevelyan. And Nevarra has only tensions with Tevinter. Tensions that the Inquisition constantly alleviates. The connection with Cassandra will keep Nevarra as a steadfast ally.
Delay the inevitable what? Talks? That's all they were. If Ferelden and Orlais went to war with the Inquisition, the Chanty's support would devastate both countries. The faithful would stage an uprising against their lords. Ultimately, Orlais and Ferelden had no power. They can't protest the Inquisition merging with the Chantry, which is clearly more of a threat to Orlais and Ferelden than the Inquisition remaining independent. Which means their dictates were backed by nothing but empty threats.
And let's not lose sight of the real truth here, the truth that BioWare was trying to keep us blind to with their false choice. The Inquisitor should have been able to convince both countries to allow the Inquisition to remain independent through the presentation of evidence, through diplomacy, and through common sense concessions. The only reason we couldn't is because BioWare is lazy and wants to funnel everyone into the same outcome.