Because, as far as I can tell, ME scientists and engineers concluded that, for some strange reason, it's better to have a slow and easily dodged missile that will shrug off attempts to shoot it down then it is to have a fast and difficult to target missile that is easy to shoot down, if you could target it.
Also, ME doesn't use computer guidence systems at all. That would be too close to an AI, after all. So their "missiles" are actually unguided rockets. Once launched, they go in a strait line, and only in a strait line.
Making the missile artificially more massive won't make it harder to kill, though. It'll still blow up fine if you actually hit it, and if it's massive
enough its own gravity well will tend to attract a near miss... While making the missile Very Fucking Fast™ is going to reduce the likelihood of a successful interdiction by a massive amount, especially if you make it low mass enough you can have it jinking around like a flea on meth on the way in
And unguided missiles are even worse than very fast rocks, in my view. Based on this sort of thing, humans by the time of canon ME should have absolutely
slaughtered the Turians unless they were completely overwhelmed by sheer numbers. Remember that back in the early
1970s we had designs for missiles that could accelerate at over 400g as last ditch interceptors for incoming ballistic missiles. That one, the HiBex, wasn't actually fielded, but the Sprint missiles which accelerated at over 100g
was, and it was doing this on chemical rockets... And it used a small neutron bomb as the payload, too.
200 years of development of this sort of crazy weapons system should have produced some fairly impressive stuff
This bit is not really true. There's nothing stopping a ship in space rotating at any angle from its direction of travel, firing and then rotating to whichever direction it wants to accelerate in now. You could quite cheerfully skate sideways across the bow of your opponent while firing your spinal weapon directly at them and even if you engage your main engine while you do so you will only find yourself curving around in a circle around them.
You could in fact circle your opponent using only your lateral momentum and main engines while keeping your spinal weapon pointed directly at them the whole time if you get your acceleration right.
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.
Economic considerations? You could build an antiship missile with the maneuver capability and sensors to dance around fighters. But if you did, it would cost at least as much as a fighter. If you want to fire a lot of them, it's probably worth cutting down to a more basic weapon...
Economies of scale should make such a thing a fairly minor problem. A lot of the cost of a fighter after all is going to be put towards keeping the pilot intact enough to get them back after the battle. Removing all of that would make the missile much cheaper than the equivalent fighter regardless of how much it ended up costing. After all, a modern fighter jet is
easily capable of pulling turns that will kill the pilot instantly and handling it without trouble, but because pilots tend to complain about this, it's limited to only a few g. Take the guy in the seat out of the equation and you could make even an F-22 turn about four times as hard quite happily...