Your argument is one of false dichotomy. It is not mage OR melee, it's both. A Red Mage without melee capability is called a Scholar. If you don't believe me go check their spell lists, everything *mage* RDM can do a SCH can do better.

I've made several posts about this, basically boils down to "fix all the above" as Red Mage should function as a party support, as magic damage or as a melee job. It shouldn't be the best in any of those categories, otherwise it would be broken. Problem now is that it's so bad in all those categories that there is absolutely no reason to ever bring a RDM to anything. A result of SE over-buffing SCH and BLU while ignoring RDM.