FFV: Dragoon- Knives, Spear
FFVI: Mog isn't a Dragoon, he is classified by SE as being a Dancer/Geomancer.
FFT: Lancer - Can use Polearms, Short Swords, and Great Swords. Can use Axes, Katanas, and other weapons given via the "Use: Weapon" skills.
:/ Sorry but Theres no game in the series that has Dragoon limited Specifically to Spears. Dragoons primary role in battle (which is all this job system is going to implement) is Jumping, and maybe things like Lancet, Cherryblossom, and other dragoon skills borrowed from Freya, Kain, and others.
So If I prefer to depict myself as a dragoon because the playstyle allows me to use things like Jump, Lancet and a Wyvern pet. But I get into a situation where the monster I'm going to fight is horribly resistant to Piercing Damage, I have to break my entire character to pull out a weapon it doesn't resist, Maybe Great Axe. so now I'm using a great axe but I'm no longer a dragoon and can't use the skills that are dragoon only. I'm no longer the character I built to depict myself.And to be honest, if a drg could use other weapons but not be good at them then whats the point?. jobs are meant for party play, for specialization...so why would you want to be sub par in a specialized role?
Once you have Jobs Unlocked your equipped job should be your playstyle. It takes over for declaring what skills you can equip, which ones you are excel at using, and grants you bonuses for using them. But none of that has anything to do with what weapon I have equipped.