The mechanics work that way because that's how they built the characters. Aside from Salarian Engineer, there is no "support" class. Even then, they pretty much are only effective against Geth.
I see the Asari Justicar being much more viable as that support class against Cerberus/Reapers with her biotic dome. Play with an Asari Adept to just spam throw while Justicar spams Reave. That's what people do anyway with Drell/Asari. Only difference is the Justicar has that dome which sounds like it'll be really useful for objective rounds.
It isn't how they've built the characters, it is the game mechanics only further reinforced by the reward system.
You have to kill to win and killing faster means more money.
For a support character to work in this system it would have to buff the damage of the entire team while still having great base damage itself, to the point where it would make more sense to pick that class than another damage dealer. They could make a class like that---but then you'd just have four of them on every team.
Support classes are generally there to help you survive what would otherwise wipe your team. Those 'surprises' don't really exist in this game, and when they do happen anybody can use a medigel. Instead you've got teams who know exactly what they're facing, exactly what they'll have to deal with, and they build for pure DPS so that they can chew it up as quick as possible, which also happens to yield the best rewards---both per match and by allowing you to play as many matches as possible in a given period of time. We're not just talking DPS, we're talking CPS(Credits Per Second).
The reward system goes out of its way to punish the more flexible, support-oriented builds.
