Pirates are already classified as machinists (gunslingers) or warriors and marauders as is, not back stabbers.
Berserker is kinda already in Warrior, just in reverse with that skill that does more damage the more health you have.

Ranger just sounds like summoner with a bow.
I feel like Dancer could've done what your shaman (green mage i think it is?) does as a healer >n>
Necromancy is a forbidden magic like Ultima so that's essentially zero, even for the Warrior of Light/Dark, also, what's Black Night?
Yeah...mounts don't exactly fit in here in terms of combat, at least not story based combat anyway. Look at the Main Story Quest raids if you've gotten that far.

So....a Warrior without an axe?
"Bladesman" is basically a rogue/ninja.

There's a reason why Arcanist is the only job that can go either way, because both summoner and scholar are still pet reliant jobs stemming off arcanist being a pet reliant job as is.
Besides, having such a system bodes problems down the road (like Scholar having a lot of highly unnecessary skills in their kit because of Arcanist's base spells, while Summoner has no need for Physick for example, but it's there because the base class can become a healer and that's the main heal of the job).

Arcanist is still classified as dps because you can't exactly be a "healer" if you only have 1 heal in your entire kit and everything else is pure damage or damage support (Rouse, Sustain, dots, a dot spread, an instant cast, and a damage field).