Do you also think the multiplayer characters suck?

I could recommend trying a couple ideas:

Human engineer - Get the freezing ray so that it freezes the environment. You can basically freeze doorways, corridors as well as freeze enemies directly. It's fun to combo enemies when they run towards you freezing themselves. And the turret can help in it as well.

Salarian architect - Slightly harder to do well, but you can use the barricade as a weapon. Give the barricade shocking power and you have an easy primer. Just get close to enemies, shock them with barricade and combo with the VI or incinerate. Then just shotgun them 'til they drop from behind the barricade.

Asari Duelist - Her ability to warp through walls and barricades are great. And when you melee with her, instead of just poking enemy with her sword, she warps slightly, making her basically invulnerable for a short moment. And if you have the skill where you get some of the shields back with every hit, she's is incredible strong flanking fast attacker.

Asari Sentinel - Fully boosted backlash is fun. You can also use her to protect friendlies behind the cover for example. She can even bounce back Ascendent's attack at him.

There many more, but those are the ones I can think of the top of my head this fast that are a bit more uncommonly seen in use. But I understand what you mean. I think one reason for it could be the number of snipers in missions. So many likes to use Vanguisher and infiltrators because it is too easy and I think because of that, many characters feels useless. 

@Tuinbonen While Asari Adept is good for running around and comboing, I personally see Krogan Gladiator more as a crowd control. She can use the annihilation to make unarmored and unshielded enemies to hit the floor and pull to get enemies close for the easy kill. I suppose she's not as fast at killing though because of that