I hit 60 on my MCH just before Stormblood released. Once I hit 70 on my main, I decided to level MCH next and, not remembering the proper item level for Sirensong, entered the leveling roulette while woefully undergeared. The first boss's unavoidable group-wide AoE one-shot me every time. And of course with how little DPS I was contributing, it cast that AoE a lot.

In conclusion: There should definitely be item level requirements for leveling dungeons.