The people in FFV were classless, they crystals gave them the skills and abilities of warriors who *had* specific classes.

Perhaps "normal" NPC type people had to train into a specific Job, like learning a skill or a trade, as they didn't have the luxury of a crystal to give them instant mastery, or indeed to be able to pump them full of multi-class levels, etc.

An NPC would decide what he wanted to do with their life, and train into that Job for the rest of their life, as their career.

The Warriors who's souls were in the crystals were simply REALLY good (masters) at the jobs they did, and had heroic destinies or some such - therefore their souls were suitable for that perpose of being stored within the crystal.

Our heroes of FFV didn't learn a Job when growing up, yet the crystals gave them all the expertise of the Warriors who did - naturally even the heroes themselves had to train to use their new Job knowledge efficiently - which is why they had to gain AP and level their Jobs up, to the maximum potential as demonstrated in the original Warrior who's soul was now in the Crystal shards.