OK, propswinger, I see your point.
If you keep the crab on all the way to touch down then I agree, you would be tracking the runway centreline but touching down with side loading.
In your scenario, the facing of the aircraft is changed by rudder, which does not change the direction of travel of the aircraft, just the direction it's facing, so that you land with the aircraft aligned with the direction of travel.
All well and good, but my point is that after removing the crab angle, there's a period of time when the aircraft is now drifting sideways - pointing parallel to the runway, but developing a lateral component due to the X-wind.
Depending on the strength of the x-wind component, the inertia of the aircraft and the length of time that the x-wind has to act on the aircraft, this may be insignificant enough not to be a problem - as you suggest - but on the other hand it may be very significant indeed.
FBW