Nitpicking...
we don't really have any jobs that have both spells and weapon skills, it's one or the other (white mage has no staff/club skills, only spells) for example.
For support purposes, there are physical attackers with actions classified as "spells".
PLD has Clemency.
BRD songs are all spells.

Granted, PLD only has one spell (two if you count Stoneskin, three if you count how Flash costs MP) and BRD songs really just have the spell classification to force cast time (action delay) and make it so that you can't do anything to sing faster. I've never tried stacking spellspeed on a BRD, and I don't intend to, so I don't know if that works.
If you were to count -any- MP usage as being spell/magic usage though, then DRK would be a great example of melee and magic.


As for all of the talk in this thread on how they'd implement BLU without a Learning ability, they could pretty easily do it.. We just probably wouldn't like it.
Learning could be classified as a General ability so everyone has access to it, even without unlocking BLU. Pop the skill for a temp buff, making it so that when the monster dies, there's a chance of some kind of monster essence loot--mechanically, this would be the same as Rogue's Mug ability. Each job quest to advance BLU would require you to turn in a set of essences, especially to even unlock the job, guaranteeing a functional set of basic abilities.
If they wanted to go an extra step to make sure you can't have an underskilled BLU in harder content, they could probably make each job quest a level cap unlock as well.

What I wouldn't like is how, given a list of recurring blue magic in the series, some of these abilities would require farming bosses in dungeons and raids. And the devs have been trying hard to keep older content relevant...