For those of challenged imagination, look at it this way: a groove wall with lateral deviations will push back against the stylus (yes, that's Newton's first law). The shape of the stylus will affect the direction of force exerted on the stylus, which just a little painless thought about vectors will make obvious. Image pushing your finger in a horizontal direction against a plane inclined at 45° to the vertical. Your force will be equally divided into a lateral and a vertical component, and the inclined plane will move not horizontally, but in a direction 45° above the horizontal. Those vectors will mean that a rounded stylus profile will experience not only lateral pushback, but also some in a vertical direction. That will tend to make the stylus go up and down, just like the chatter on a machine tool. A stylus with a side profile that is more vertical, will experience that force more in the lateral plane and less in the vertical.
None of this will matter more than it does with a stereo record and a stereo cartridge, as long as the mono cartridge has vertical compliance. If you have a mono cartridge that has no vertical compliance, all that vertical force has no suspension to damp it: it must make the whole stylus/cantilever/cartridge move up and down with the resulting hammering in the groove. This seems rather elementary.
Now you might argue this - but what does vertical chatter matter if the groove only contains lateral information? Sure, we can go there. Conical styli used to play mono records for many years in the days when mono cartridges never dreamed of having vertical compliance. Did those records suffer more damage than a mono disc with a non-vertically compliant cartridge? Than a similar cartridge with an elliptical profiled stylus? Or a stereo record with a stereo pickup? I don't know, but I can see the theoretical argument for why this should be so.
This does make me feel more likely to settle on a cartridge that is an adapted stereo design, with its guts rotated 45° and with a modern profiled stylus. That way I'll do no harm if I accidentally put a stereo record under that pickup, and I know I'm theoretically less likely to damage my original mono Parlophone Beatles.