This whole concept would be terrible for the game as a whole. People who like tanking could play only tanks, people who like healers could only play healers but then damage dealers would have a bare minimum of 3 jobs (Bard, Black Mage, Monk) and some people might not like even one of those.

The balance between jobs right now (while it could use a tweak here and there) is pretty good and that system would make said balance take a huge step back. Dungeons could indeed use more difficult challenges, more depth to the encounters but this proposed system is absolutely not the way to go.