> tries to explain why quantum mechanics is mechanics

Curiously though, since the 1800s analytical mechanics, too, began to be seen as a branch of mathematics. But I think that in this case, just as in the case of quantum mechanics, it is still extremely important to see the physical content, and the physical principles, that allow us to apply this or that mathematical framework. The fact that physics is a heavy user of mathematical methods (probably the heaviest of all sciences) does not mean that it reduces to mathematics. Don't lose the forest for the trees.