I am unsure how to interpret your post. I thought that the RMS voltage between two phase conductors would be unchanged if one was grounded or none grounded. True, the peak voltage is 1.4 times the RMS voltage, but this is again unchanged if none or one is grounded.
If these conductors are in a conduit, and you ground one, the effect on the others is hard to predict. If the conductors originally were all "floating" at about the same voltage from ground, then the effect of grounding would be to increase the voltage stress to ground on the other two. But, since the RMS and peak voltages between these conductors is unchanged, I would expect no difference in the probability of an insulation failure occurring.
If you are looking at equipment terminations where the conductors are further apart, yes, the increased voltage to ground could cause another fault.
I continue to believe that two phases short circuiting to ground almost always happens in sequence, with the first fault to ground occurring a significant amount of time before the second. Of course, there are situations where a fault from one phase to ground (in a grounded system) produces enough heat to vaporize everything in the power distribution equipment, but does not draw enough current to trip the upstream circuit breaker.