About the gameplay:
-Remember when they didn't allowed the BLU in common raiding due to broken abilities/people not having all the skills that could be usefull to the group? Same problem, different form, you would have a "BiS" monster and you need this monster.
-We already have a job focused on Summoning, buffing and healing, it's called Scholar. There's also another job around Summoning that is Summoner and you might not remember how dreadfull the pets abilities were and how annoying they still are.
-Looking at how you describe it, it would be a limited job. Do you remember how people loved when BLU was released?

Lorewise:
-There is a Necromancer job in FFV, but that one only summoned demons, using Dark Arts to cast Meltdown, Deep Freeze Dark Flare, Chaos Drive, Doomsday... DPS abilities. It's a Darker Black Mage and SQEX would probably choose that direction.
-Warrior of Light, Necromancer. Storywise, the WoL tried to stop many Necromancers spells or simply defeat a Necromancer. Think about the first Deep Dungeon. While Dark Knight exists, SQEX tries to give the idea that Darkness is a tool, an element, not the Evil. Like fire, if you play with it you burn yourself. Necromancer, however, is often associated with Death, Inhumane, Immoral and Evil, they bring back deads after all!

In short, it's a possible job but it probably won't be implemented the way you want.
The idea would fit in a Sandbox MMO. I've seen plenty using this system and let's just say it was annoying, boring, repetitive, so broken they had to limit the "capturable" monsters and did not worked at all.