The requirements for Memory would quickly grow out of control, making it incredibly difficult for players to boost any stats other than Memory if they wanted to use higher tier skills.
Even with bonuses to Memory from items (and personally, I think that
Memory should be on items only in rare cases), that would result in players picking their gear based on if they can maintain or increase their amount of Memory.
I think instead that different Tiers require you to have more points into the required Ability (and the skillbooks cost more with each tier). Tier 1 skills require [AbilityName] 1. New skillbooks appear at level 4, those probably could be considered Tier 2 and require 2 points in the ability.
I don't think your idea of increasing requirements for Memory is totally off the mark, though. I think Memory should increase a bit slower, I think, maybe +1 slot required every 2 Tiers instead of +1 slot every single tier.