I have lost hope that they will fix this issue by now. Maybe if they ever decide to make a remaster, but BioWare hasn't made remasters yet and EA has only done so very rarely (Burnout Paradise).
There's a mod that fixes the issue: https://www.nexusmods.com/masseffect/mods/71/?tab=files
@wingedrunner and additional to @Fred_vdp
While I see how that is annoying, you're right, the culprit is that AMD decided to discontinue its own Instruction set AMD 3DNow after 2010.
It would be easy for them to keep it for backwards compatibility, but they decided to put it on the software developers that used a AMD technology...
For the rest, I agree with Fred. The only way that this get fixed is if they decide to remaster Mass Effect.
