A great question! Are they necessary? No. Are they highly important? Yes! You can grind your way solo if you really want, but it makes life that much more boring and slower imo. It does help if you get lucky and pull some of the top characters from souls early on.
Basically troopers serve 2 purposes:
1) Good troopers will help you progress the game faster, keeping things more interesting and gaining better resources for your own players.
2) the trooper points can be invested in skillshards to improve your characters, or souls to find those rare killer new characters (plus get a lot of crap & duplicates along the way too
In your case, if you hit a roadblock, I'd suggest finding troopers with great characters will really help you. Both, in that you will more likely clear the levels, but also you can check out their talisman builds and get a feel for what you can do with your characters.
Also, skillshards on the right toon can really help ramp up their damage.
The other advice is to go back over levels. Clear all the skulls in past levels so you get the secret locations. They always give the best drops for building your team (and the best gold).
Otherwise, keep posting here for help! If you give us your in-game name too, we can check out your team and make suggestions on what to focus on with developing your team too.