I was trying come up with a new paradigm for classes and race design and was considering using tier as a progression. At this point though, "proficiency bonus per day" is a more and more used mechanic and I think that adding tier in there too ads a needless extra layer. I'd run with prof bonus per day or half prof bonus per day to keep things elegant and congruent.How about as many times as the Tier they are in?
once at tier 1, twice at tier 2, etc.
thiugh I really think there should be a way to make it a bonus action too. Maybe at tier 2? Or 3?
It seems okay to me, but the place to look for unforeseen consequences are other abilities that key off breath weapon uses. The Dragon Fear racial feat is the only one I know of, but it's possible there might be some 3PP stuff in your game.I was mostly concerned if there was some unforeseen consequences I hadn't considered.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.