I'm not a master tech but I did fight this a good bit on the E36 and can give you my anecdote. The e53 has so far been very good in this regard, even before in a state of neglect, and still after I have messed with it extensively the wheel doesn't vibrate.

The E36 was initially vibration free, and then I went about replacing some blown shocks and control arms and the oil pan etc etc. Tore apart the whole front end. First drive the alignment was way out, and once I hit 55 mph the wheel was kicking back almost an inch.

I did the string alignment, and after three times to get that exactly right, it did help a lot but still on certain surfaces at a certain speed the wheel had a little shake.

I ended up cleaning and redoing the front brakes, not really replacing anything, just cut the rotors ( yeah I know ), clean the guide pins, lube where TIS says to (not the pins), and make sure everything was really clean and even. That helped with some clipping noises and some vibration that was appearing under braking, but the wheel shake remained. I don't think I torqued the calipers all that correctly at one point.

The issue was the sway bar and how I installed it. On that car it has to be torqued evenly on the ground and I just sent it with the wheels in the air, which I knew was wrong but didn't think would matter much. I redid that with some new end links, torqued it per TIS on the ground with some weight in the seats and the wheel is perfect again, the thing drives great.

So perhaps it's something with the sway bar end links or the stiffening plate which hasn't been mentioned yet. If you reuse those bolts a bunch they don't clamp and that could create some sloppiness. I initially came here to post guide pins as just suggested above.

__________________
'05 E53 3.0 6mt
'17 F30 340ix 6mt
'96 E36 328is, in progress