Tiered dungeons like that tend to be problematic. Mythic had a shot at it with Warhammer Online, but it backfired on them quite hard.

To avoid being boring, content needs variety. If you have to repeat the dungeon A a lot of times to access dungeon B, and then dungeon B a lot of times to acces dungeon C, the process becomes much more tedious for most player than just being able to access dungeon A, B and C to begin with.

Basically, you created "Content X 3", and you gave your players only "Fun X 1", instead of creating "Content X 3" and giving "Fun X 3"
It's a big waste of resources compared to the result.

The only way to implement a tiered system that doesn't conduce to tedious repeatitiveness is to make the actual item needed to access the next tier drop for everyone at the first completion of each dungeon, but STILL have additional gear dropping in each dungeon. Se that the players have a choice, once finished each dungeon, to do the previous ones for gear or the next one for the novelty.