On the jewels point, cosplaying is already quite hindered by damage caps (why you only see the hitting schools and death do it). So, theres already a limit based on school to the amount of off school damage that people get.
"Why would a Storm hinder their hitting stat for another class when they could do so much more damage as their main instead?"
Cameca and other bosses that cheat cast chromatic weaknesses can have this bypassed by offschooling, or Freddie which does chromatic dispels.
"Why hinder an Ice when their damage is already bad, encouraging to pour all offense stats into legit any other school than its own"
You don't have the ice hit. Ice isn't a hitting school. This is how classes work, some are not built for hitting.
"Archmastery exists for certain spells to not be spammed"
Thats not the point of archmastery, its so you can off school effectively. You don't need mastery amulets use archmastery.
"You objectively are never going to use another class's spell on an offensive class because of less damage"
There are cases where this is done (Freddie, Cameca, Millispeeder, etc)
Overall, the point of weaving is to use the effects generated by other schools in order to bolster your own. Thats why you have the dual blades from storm, or the trap clear to weakness from dife weaving. Weaving isn't to make it so you offensively use multiple schools, its so you strategically use another school to benefit yourself.