Adding in a min ilevel for levelling dungeons is a good start, but I would also advocate for a minimum weapon ilevel needed for content as well. Since this is your main source of damage/healing, it is probably the most important piece that needs to be kept up to date.

It was just the other week I ended up in an expert roulette with a DPS in at least i390, but their weapon was only the i290 antiquated weapon and this was Ghimlyt Dark. Infact, you might be surprised how high your ilevel can be in full i390 and a level 1 weapon (my quick maths indicates about i330) which in theory can get you into plenty of endgame dungeons. Of course, this is an extreme example, but it still highlights potential problems (for the record, an i290 weapon hits about i350 as an average). My personal gauge for an appropriate weapon is it has to be at the minimum ilevel for the content otherwise it is inadequate, you could get away with a bit lower in most content however.

Priority should be a minimum ilevel for all dungeons and trials though, which should be the first step into trying to make levelling dungeons not as much a roulette on whether your team makes are up to the task or not.