I would not be opposed to this idea.... Red mage already auto attacks while casting, so being a casting job that does better if in melee range could be interesting and different. There are a few other things to adjust to this. For example, you could make this a trait that happens at level 72 and just have engagement replace displacement entirely.

It would add an additional 20% or so to red mage DPS, though, so I might expect the job would get other nerfs if this were implemented.