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.