I sort of wish players could only choose one job.

[Raagnar]

While a character's role throughout the series isn't specified, that shouldn't suggest that they weren't there. In every game, (in my experience) each character is depicted with a set of unique abilities that usually indicates their role in the party.

For example, while you can use Tifa in any way you want, her particular set of skills depicted in her limit breaks and stat advantages for physical combat allow us to deduct that she is a monk classed character. Cid, of course taking part as a Dragoon. These aren't coincidences. In all those games (Or at least most of them.) The characters all exhibit abilities unique to a particular job.

This is your personal opinion though, how you chose to see these characters. The battle system in VI and IX is very flexable and regardless of the weapon you can form the character to any job you wish. Same with VII, Its more about the visual and when you break it down everyone is some form of hybrid DD/mage. FF games with more set characters shouldnt be fit into jobs, you can make connections but thats where it ends.
You can call Zell a monk but what is Squall? you can call Quistis a Blue mage but what is Rinoa? a ranger?

My wife thinks Ash in XII is a healer, how did you use her? she was a melee for me.

Point being, a lot of this comes down to opinion and how you played each title.

[Orophin]

This is your personal opinion though, how you chose to see these characters. The battle system in VI and IX is very flexable and regardless of the weapon you can form the character to any job you wish. Same with VII, Its more about the visual and when you break it down everyone is some form of hybrid DD/mage. FF games with more set characters shouldnt be fit into jobs, you can make connections but thats where it ends.
You can call Zell a monk but what is Squall? you can call Quistis a Blue mage but what is Rinoa? a ranger?

My wife thinks Ash in XII is a healer, how did you use her? she was a melee for me.

Point being, a lot of this comes down to opinion and how you played each title.

Well actually...pretty much every FF game that didn't have a job system or something similar, like the sphere grid or license board, the characters pretty much had a set role. Cecil was a physical powerhouse with good defense and some white magic. Rosa was a white magic user that could use a bow and arrows or staves. The list goes on. You can fit each character from those games into a specific role even though they had multiple angles to them. Like, you're not going to use Cecil as your main healer, even though he has white magic, because Cure 2 just isn't powerful enough.

My take on this is the FF MMOs wanted to use the job system featured in many of its games so that people could experience every role on one character. If they wanted you to only be a Warrior or a Thief for the entirety of the game, it would have originally been designed that way. And I'm sure many people still would have played it, but this was one of the unique things FF brought to the genre.