Maybe part of the reason mages aren't strong is because...

There's no real MR items. They're all hybrid items in some fashion, or that is to say that they pour a majority of their efficiency into anything but the MR, usually into utilities that don't even counter mages any more than they do everything else. Banshee's is the only real "pure" anti-mage item, but even it falls flat because the passive spell-shield has a 40 second cooldown and can easily be wasted.

This means that without any truly decent items to build against mages, you have to keep them in check by restricting their power directly instead of offering counters.

The reason for this? It might be because map interactions and basic attacks are almost entirely physical damage. The reliance on armour overshadows MR at every turn, so there's less variety for MR than armour simply because there's no contest about what you'll use your item slots for.

Maybe if we made some minions, monsters, and even the turrets deal magic damage as well, it would make MR more prevalent, and armour less. This could even solve several issues with balancing AD champions, as without armour being as much of a threat, they wouldn't need all these special mechanics in place to reduce or ignore it for the sake of removing that layer meant for mitigating ubiquitous physical damage.