I wonder this a lot myself. A lot of people on these forums, Red Mage or otherwise, seem preoccupied with what they thought a job would be, or what they think a job should be, and not what a job actually is. Whether it's a comparison to other Final Fantasy games, facets of in-game lore, or simply the character Archetypes that each job name represents, people want the game to change to reflect their vision rather than simply pursuing the class, or the game, which has what they are looking for.
FFXI isn't the only game in the world, Red Mage is not the only job in the world. I'm not trying to push people off, but really, if the game itself is just not fun for them, they should try other games. If a job is not something they envisioned, then they should try other jobs. As far as Mage/Melee swordsmen go, Red Mage definitely takes after the Mage side while Blue Mage takes after the melee side. Have any of the RdMelee enthusiasts tried out Blue Mage? It seems to basically be everything you're asking for, just with a different color in its name.
I know some people have their sort of sentimental attachment to one job or another, and that's fine. But realize that that's all that is. It's a sentimental attachment to the color red. It doesn't have to do with you liking the job itself, because it's obvious that Red Mage in its current state is not making you happy. You just like the name. Or the idea of Red Mage.
I'd honestly really suggest Dancer or Blue Mage to a lot of Rdmelee enthusiasts. Blue mage especially, though I'll warn you right now, as much attention as the job's had in Abyssea, it's practically worthless outside and its time in the limelight is most definitely fading fast. Take that for what you will.