Steering wheel shakes when braking – could engine mounts cause that?

[marcusstoinis]

I know the usual culprit for brake shake is warped rotors, but here's why I'm confused. I've already replaced the front rotors and pads on my 2014 BMW 740i and the steering wheel still shudders when I brake from highway speeds. It's not a vibration through the whole car, just the steering wheel oscillating left and right. Tires are balanced, alignment is good, and the suspension feels tight. A weird theory from a friend: he said worn engine mounts can allow the engine and transmission to move around, which can make the steering feel shaky under braking because the whole drivetrain shifts. I've been looking into a https://bmw-garage.ae/engine-mount-replaement/ that can inspect the mounts without me having to book a full day at the dealer. Has anyone here actually fixed a brake shake problem by replacing engine mounts? Or am I just trying to avoid admitting the new rotors might be defective? Would love to hear if this is a real thing or just internet nonsense.