This poses the question of why worship the gods in the first place? The gods of Krynn are fickle and cause so much strife - just look at the world's history.
Krynn survived perfectly well for nearly 40 years without the gods during the Age of Mortals. The people discovered divine magic through mysticism as you describe; they no longer needed to prostrate themselves before the gods.
I would contest that the people of Krynn survived perfectly well. Takhisis was still there, preparing for the War of Souls. In the meantime, Ansalon was ruled by five dragon overlords who terraformed the hell out of Ansalon and made life miserable.
It took the gods, specifically Takhisis, to break their reign. Some of the other gods, like Chislev, are trying to undo the damage done to the continent.
The theme of the Age of Mortals, post-War of Souls, is that people have a choice. "May the gods guide your way, or not, as you choose."
I wonder what would happen to Krynn if the faith in gods dried up and mysticism took over? It stands to reason the world wouldn't disintgrate as it survived perfectly fine without the gods during the Age of Mortals. The sun still rose, the tides still came in and out, life went on while the absent gods tried to find their missing world.
Yeah, but the world suffered.
From a gaming standpoint, mysticism was a replacement for cleric magic. It was given some good flavor in the SAGA rules system. The mystic in 3.5 was to the cleric what the sorcerer was to the wizard. So yeah, Krynn can survive. But it loses so many themes without the gods.
Mysticism could be adapted to other worlds. Thematically, it's similar to the Force (minus the midichlorians). It's a magical power of life. It can be the source of divine magic. In 4e, you could expand on that to include primal and psionic magic too. For Dragonlance, I use mysticism as one possible source of the divine, primal, and psionic power sources. And yes, I do use the psionic power source since a few of the Spheres of Mysticism were borderline psionics anyway.