When I looked at the specifications for Iwasaki MH lamps that retrofit into MV ballasts, I found a piece of information that eludes me:

EYE MULTI SUPER ACE, EYE MULTI-HI-ACE, EYE CLEAN ACE
1. These lamps should be operated with reactor mercury ballasts. Never operate with the constant wattage type ballasts (CW or CWA).

I have seen some members saying that MH lamps seem to not experience voltage rise during life and thus they say that it is safe to operate them on CWA ballasts. With these Iwasaki lamps, I wonder why these lamps might damage a CWA ballast or the lamp?

It sounds to me these are saturated vapor, so will exhibit the positive thermal feedback.
It may not lead to thermal runaway directly (which is the only thing directly killing the lamp), but it will definitely widen all the spread leading to inconsistent color temperature (because every component from the fill has different curve describing pressure vs temperature dependency, varying temperature causes the ratio of the component in the gas so plasma to vary, varying the ratio of the color contributors), to the extend the color would be way too off from the rating. And the wider temperature spread may cause some lamps to fail earlier, flattening the mortality curve (which is bad, as for a given mortality limit, e.g. 2% in streetlights, it means shorter useful lifetime when the scheduled group relamping is the maintenance strategy used).