Al and Anis are two sides of the solution, but instead of working together to make a complete plan they are forced to oppose each other.
Algard has correctly identified that the nobility is hellbent on propping themselves up by retaining control of the most important resource, magic. They will slander, impoverish, or outright kill anyone who attempts to change this. After years of seeing their terrible behavior, he reaches the conclusion that he needs the power to destroy their power. He's going to fight fire with fire. But while eliminating the nobility would allow Anis to spread magicology and improve the lives of the commoners, it won't replace the hierarchal government with an egalitarian one.
Anis believes in the slow and steady march of technology to fix things, but she's trapped in the thinking of individualist neoliberalism. Her motivation is selfish, and the disruption she will cause is going to kill more people than Algard's coup. The nobles will use violence to curtail their loss of power. The more magicology spreads the more oppressive they will become to purge anyone who tries to challenge their authority. Just like the transition from Feudalism to Capitalism, I expect elites will first try to stop magicology from existing, then attempt to gain control of it to reinforce class structures.
I think Algard is right to try to purge the Nobility since the evolving paradigm no longer requires them. And I think Anis is right to make magical resources more egalitarian. But neither of them recognizes how an Egalitarian world would function. Neither is trying to create a cultural shift where people could accept non-hierarchal organizations. All they are doing is giving the conflict crueler, more advanced weaponry.