Every mmo in the last 5-10 years has some level of distinction between "Raider" and "Casual" Tier when it comes to loot. In FFXIV, its going to be dyeable versions. It's done this way as a quick and easily identifiable way to say "Yeah, I cleared it and got the armor." It is bragging rights, broadly. If you make the regular version dyeable, You remove that quick and easily seen bragging right from players who are doing the content.

"But who cares about their bragging rights! Internet points are stupid!"

Problem is, people do like to show off their accomplishments, and status is a thing. If you make it so that there is no distinction visually from raiders and casuals, a lot of raiders will simply say "Screw it, why do the content when I can just phone it in on the regular side and pretty much reap the same rewards". At that point, having savage/extreme gear only matters for the sake of doing more savage and nothing else. On that model, people will more frequently not apply the effort since its self fulfilling. At least with it currently, people who want a glamour reward to show off and have something they can customize will put the effort in.