With the GTVA spanning such a wide expanse of space, a sizeable active fleet is needed simply for policing and security.
Just as a police force (or militia) is necessary for cutting down crime on land and a navy and airforce are necessary for cutting down on piracy and smuggling, the GTVA would require all fleets to maintain a pretty good level of combat readiness.
In space im guessing the requirements are more taxing. Even old Valkyries, Apollos, and maybe some hercs could do serious damage unless their targets were protected by a superior force. Superior because an equal force would take casualties, a fighter or two would slip through and kill lots of civvies (only one hull breach is necessary to kill pretty much everyone on the deck in space)...etc.
That, and to simply maintain a military deterrent on local governments. after the chaos of reconstruction (im assuming chaos existed), terrans would want a powerful deterrent in place to stop regional and local skirmishes.
A single Fenris, allowed to get into orbit, could do serious devastation to a city with an orbital bombardment, not to mention if the rest of the local defense forces could do bombardments too.
Therefore, the GTVA would keep a strong military in order to quell all of these possible conflicts. SO they would have been reasonably ready for the Shivan advance (should it have come), without having to take all of the losses from the NTF rebellion.
remember, they lost 75% of the 6th fleet in Epsilon Pegasi from Adm. Koth's attack. Thats 75% that could have been used to, say, protect the Capellan exodus convoys. Wouldnt YOU have liked an Aeolus, or at least a Leviathan or Fenris on the Exodus mission?