Only in pathological cases, which is what your examples are all about. When comparing two amplifiers, one decent and one pathological, the difference you reported is totally irrelevant, since the standard THD values are already two orders of magnitude (or more) apart. It's called "engineering", you know; engineers know when to ignore second order effects.
If there are substantial differences in values, yes, I agree, this discrepancy is second-rate.
But if the THD and/or IMD values of two amplifiers are comparable, let's say they differ by less than 10dB, you can't tell if in fact one is better than the other if you don't know the order of the distortions that caused them, since the mistake you make depends on them. In other words, a classification based on THD or IMD loses some meaning. Even the SINAD, which should take into account all the different energy components, is missing pieces.
Anyway, these numbers are not the most important aspects to me: it is much more interesting to observe the distribution of energy among the harmonics to understand the sound quality of a device.