It didn't begin in the 70s, that was the point where it tipped into large-scale violence. More important, though, it wasn't "friction between Muslim south and Catholic north", it was friction between indigenous populations and settlers, both in the south. In many ways it's better to speak of conflict between settler and indigenous populaces and remove the religious aspect altogether, because ultimately the conflict isn't about religion, it's a fight over land and political power between indigenous and migrant populaces.
The first great mistake the government made was to try to alleviate agrarian unrest in the north by opening the south to sponsored settlement, without considering the potential impact on the south. That mistake is essentially irreversible: the settlers aren't leaving. The indigenous populace - now a numerical minority in many areas they traditionally controlled - wants the future to be decided by them: they see the majority as an imposed condition that should not be allowed to dictate terms. The settlers - many in their 3rd and 4th generations, some more - don't agree.
The second great mistake the government made was when the violence between settler and indigenous militias broke out, they took the side of the settlers instead of trying to act as a neutral mediator and law enforcer. That might theoretically be reversible, but realistically it will take generations: trust is easier to break than to make, and the Philippine government has little credibility as a neutral mediator.
The third great mistake came after the fighting reached a stalemate and government bought a window of peace by buying off key insurgent leaders with lucrative government posts. That offered a window of opportunity for government to step in and govern, but the window was not exploited: government preferred to offer unlimited license to steal and abuse to anyone who could keep the peace and deliver the votes in a given territory.
There have been others, including the disastrous failed "peace agreement" that we saw recently. I don't see the fight/talk/fight cycle changing any time soon. I am definitely curious over what form the next incarnation of Yakan/Tausug insurgency will take... there will be one, almost certainly.
OT here, but again I think you're drastically oversimplifying the sources of AQ influence, and perhaps adjusting them a bit to fit them into your model.
Many Filipinos do blame the US for their situation, with some reason, but it's more a left narrative than a Muslim narrative. Every place is different.
In Indonesia and the Philippines jihadi movements have drawn their support not from the global AQ narrative, but from local sectarian conflict. They've done this with limited success. Support in Indonesia has been sporadic, limited, and closely linked to outbreaks of sectarian violence. There's little evidence that the jihadi narrative has ever had much pull in the Philippines: the ASG never drew popular support until the KFR business started drawing in money, and the JI connection is primarily opportunistic, not ideological.
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