Greetings, John (vanstoja) !
I believe that for horizontal motors the shaft will be off-center low within the bearing, but this is compensated by setting the bearing off-center high within the end-bell, such that the rotor is roughly centered within the stator.
You are right that centering of the rotor shouldn't change by itself, only if not set up properly from the factory or during subsequent dissasembly/reassembly of the motor, so malfunction is probably not a good term. Normal bearing wear might allow the rotor to drop down no more than a few mils.
My impression is that foot-related conditions are more common source of 2*Electrical frequency for small horizontal motors perhaps 100hp and below. For larger horizontal motors with stiffer frames and perhaps more care in installation, foot-related distortion does not seem to be a big problem and the less-common air gap problems from other causes would be more likely the cause of 2E.
I have not encounted many electrical-related vibration problems in vertical machines using the pivoted-pad radial bearings. The closest I have seen is one example of large vertical motor with pivoted pad bearings where I had a very strange pattern of 2*LF with running speed sidebands
I was aware that the general reason for using these tilted-pad radial bearings was to avoid oil-whirl type problems in vertical machines where there is no radial load to enhance stability. On our large vertical machines there is typically somewhere around 5 mils clearance at each pad (machines have air gap on the order of 100 mils). Can you explain what you mean in your last sentence? Are you saying that we expect around 10 mils of radius of shaft movement during normal operation?