I find that an interesting view on the situation. The situation is completely different now. Suharto is gone and the governments after him have changed.
Until at least 2004, prior to the tsunami, the Indonesian military was on the ground, killing locals. They stopped once the eye of the world was upon them, once they had to come to some kind of reconciliation due to the unprecedented nature of the disaster. I have multiple relatives who were harmed by the Indonesian military, some of them not even associated with GAM.
GAM has signed a peace treaty and RI troops have withdrawn. There is an agreement over Aceh's natural resources and also an agreement that give the Aceh quite a big deal of autonomy to organise and rule it's province how they want it. The situation is more or less stable, economically and socially, so most families can live in peace and raise their children without having to worry about severe poverty, a civil war or anarchy. On top of that Aceh enjoys the safety of an army that protects it against groups or countries that want to harm it.
Why support separatism and risk all of the things above?
It's true that the Acehnese people are tired of struggling. Even a population as tenacious as the Acehnese need stability. They have not stopped desiring some kind of independence, however. I know very few Acehnese who support remaining part of Indonesia as it stands today. Like all people, they have differing views on how this can be achieved. Some are staunch separatists, who would see an independent Aceh. Others believe that Sumatera should be an independent state. Very few Acehnese, or other people indigenous to Aceh, take a positive view of remaining part of Indonesia.
The Acehnese have a right to self-determination, no matter how ill-conceived that vision may appear to be. Before the term "Indonesia" was ever coined there was an Aceh, and it was likely the last independent stronghold of a Chamic people in this world. It's special, to them, to me. Acehnese people are my loved ones, my relatives, my family. If Aceh remains part of Indonesia, it will suffer the same fate the Acehnese and other natives of Sumatera have seen in the east of the island: transmigration and slow destruction of the indigenous cultures that live there.
What risk is there in supporting separatism? Aceh is still poor, still developing. If they left Indonesia it would be a lateral move at worst, and I argue at least then they'd be fully in charge of their resources. Indonesia does not "defend" them from anything, Aceh has no fear of foreign foes other than Indonesia at this time. I honestly cannot imagine any real benefit to staying part of Indonesia.
The reality is that Indonesia will not let them go, not without a fight. The real question is not "why support separatism,"
the real question is "why can't Indonesia let them go?"