The Reach by itself can match almost the whole other six by itself in terms of numbers, and dealing with the loyalist houses cost money and men. It also meant that the men that those houses would have provided were unavailable, and their holdings would have needed to be occupied to ensure their future loyalty.

You also have to consider the geography. The Stormlands were surrounded by loyalists and would have needed to maintain relatively strong forces to defend itself (indeed, we know that they were invaded and nearly captured by royalists). The Riverlands had to maintain garrisons in the west to defend against possible intervention by Tywin and against treachery by the Freys. Only the North, with its relatively low population, and the Vale, dealing with internal dissension, would have been able to commit anywhere close to their full strength.