Well, there
is something stopping this being practical, this being your thrust source. As I understand it, the mass effect drive isn't actually a drive in the normal sense you're thinking of, it merely lowers the mass of the ship to the point that
Magic Happens™ and it can somehow accelerate past the speed of light. The actual
thrust is produced by a fusion reaction drive, or in some advanced ships later on, by an antiproton drive. These are still rockets, and the main engines are going to be at the rear of the ship, producing a vector through the centerline. It's certainly not going to be set up to give omnidirectional thrust at the same power level, at least based on every image of a ME ship I've ever seen. Manouvering thrusters will allow you to turn, yes, and slide sideways, but
not at anything even remotely close to the level you can accelerate on the main drive. And the ME field doesn't as far as I know entirely remove inertia, it just reduces it massively. So put together this means that if you're accelerating hard, there's a distinct upper limit to how far and how fast you can shift direction, especially if you want to keep your ultimate vector pointing at the enemy.
Plus, remember, the shots are completely unguided and unpowered. Once they leave the mass driver they're subject to normal inertia, so if you
do have a vector that's got sideways motion as well as forward motion at the time you fire a shot, the projectile will
retain that combined motion, and track sideways relative to the target. You're either going to have to compensate for that by firing off in the other direction and allowing the vector to bring your shot on target, or aim directly at the guy and have no off-axis motion at all. Which, again, means you're both going right down each other's throats
All the video I've seen of battles in the game show the ships firing in dead straight lines at each other, so logically they're doing the latter method.