Riot should just do away with mana as a resource all together.
Take a page from Dawngate (RIP) and come up with a resource on a champ by champ basis that limits the champion's abilities in a meaningful way. It's clear that having mana, energy, and resourcless types of champions is extremely hard to balance.
Instead of constantly juggling a resource like mana for all types of roles against champions with no resources at all (or energy), just do away with mana and mana regen items, and gate each champion's abilities in a way that makes sense.
You'll never have a large number of champions viable competitively until you make some sort of change like this.