You definitely don't need to start over. You're not so far along that you can't get back on track. All you'll do by starting over is lose the free 3* Bossk you got from the marque event and have to farm everything else you do have over again.
The whole Tank/Healer/Dmg Dealer thing is basically true, but not all the time, so don't get too caught up in what each toon is classified as. Different factions accomplish these things differently, and synergies usually work with faction tags rather than classifications like Tanks/Support/Etc. The game breaks down into 3 main areas IMO, and they're the 3 things you should focus on when deciding what to farm:
1. Legendary Characters
2. Arena (squad and fleet)
3. Raids
There are other areas of the game obviously, but these should be the main things to look at when farming. And #1 is a big part of both 2 and 3.
This is the main reason why Phoenix makes such a great team to farm early. They have great synergies, they can be ok in arena, they help with GW and TB, but the biggest thing is that you can get 2 legendary characters with the same team. They get you the arena meta leader (Palp) which you can get with any rebels, and they get you arguably the best all-around character in the game in Thrawn (also part of the arena meta), which you can't get any other way.
So while you don't have to start your account over, you might want to halt your current farms and start focusing exclusively on Phoenix right away. It might be painful in the short term trying to get by with the current mixed bag you have now, but once you get them in place, they can really jump-start the rest of your roster. I was in the same boat with my alt and had to do the same thing. I'm loving that account now, even though my Phoenix team is largely unused.