Summoner: Summons creatures to aid the party in battle. FFXIV's SMN does this.
Red Mage: Casts both black and white magic, battles with swords. FFXIV's RDM does this.
Dark Knight: Heavily armored, battles with Great Swords, uses Darkness-based attacks. FFXIV's DRK does this.
Dancer: Dances to both harm the enemy and buff the party. FFXIV'S DNC does this.
Main Series Chemist: Mixes items in the inventory to create various effects. I don't see that working in XIV as it requires consumables to work.
FFT's Chemist: Throws healing items = Useless in XIV. It's an initial job you use because you have no other viable means of healing people at that point in the game. Chemist abilities literally just unlock which items they can use. A starter Chemist, for whatever reason, has no idea how to drink or throw a Hi-Potion because I guess the glass vials they're in are more sophisticated somehow.
Players are upset about BLU because it's a Limited Job more than anything else. The reason they want it changed is so it can be a traditional job that can be used in all content. Again, this has similar issues because doing so runs the risk of stripping the job's identity down to the point where "It dresses like a Blue Mage, but that's about it." BLU is a little less dramatic because, I suppose, you *could* rework the job. I'm just not exactly sure how.