The counterpoint is flawed by the environment in which it's been experimented. Excessively easy mobs make the differences less evident.
You can dress your mage up in heavy armor, but he will receive much less protection from that armor than someone with the preferred class. If your mage dressed in heavy armor can tank effectively, the problem isn't that he can wear heavy armor, but the fact that the mob doesn't hit hard enough (or that the difference in bonuses between favored classes and non-favored classes isn't high enough)
Ultimately, you can dress your mage in heavy plate armor, because your mage has a body, and heavy plate armor tends to fit a body (I dabble with heavy armor, and I still haven't encountered any that tells me "NO! You're not fit to wear me! Begone!"). He isn't necesssarily proficent at using it though, and it's appropriate that the protection he'll receive from it will be limited.
Other differences are rather evident. Mages can't use heavy shields, resulting in a much reduced protection from them (barely justifying the stamina used for guard just when they solo).
Non casters can't use any AOE effect with spells, and ultimately the effect of every single ability not belonging to the equipped class is limited by class affinity.
So yeah, the differences ARE noticeable, and would be much more noticeable when experimented in an environment that challenges them to the limit.
The only real problem is that the FFXIV environment, at the moment, does not challenge the player and his abilities to the limit. It doesn't even get near to that.
Hell, I can easily tank anything my group throws at me effectively with one hand on the joypad and the other hand holding the coffee cup, as I watch anime on the second PC. And I'm sure I'm not the only one.
This means that even seriously gimped abilities/defence/attack are still sufficent to fullfill a main role.
Add the challenge, and the abilities will become sufficent only for limited support/soloing, and there you have your class uniqueness. Without the hassle of removing any kind of class flexibility (that many enjoy) from the game.