Seems to me that "dynamic headroom" is just another term for transient response capability, which is a more well known terminology in electrical engineering circles (at least for SATCOM systems), especially for power amplifier design.
That's the thing I am having trouble with, the definition. However, Jean did define what dynamic headroom is for the purpose of this thread. I am not clear if 'dynamic headroom' is the same as 'dynamic power' that is often used by manufacturers such as NAD and Yamaha though. Based on that definition, I absolutely agree when shopping for amplifiers it may be better to consider amplifiers (mid range and up) that show lower dynamic power/headroom? because manufacturers who emphasize their higher dynamic numbers may in effect skimp on the transformer side but put in more gigantic capacitors or other clever technique/features to boost the extremely short term rating to impress the potential buyers. The entry level NAD C375 is a good example, relatively lower continuous power rating such as 2X150W but very good dynamic power rating, though they don't specify their definition of dynamic power. As such, we have no idea whether it is for a duration of less than or more than 100 ms. There is indication that it is for 20 or 200 ms but I am over simplifying it here. I can send you a link if you are interested.
Back to the OP's point, my only main disagreement (respectfully) with the him is that, if two mid range real power amplifiers have the same rated continuous power ratings, the one with higher dynamic rating is not necessarily indicative of having a weaker/cheaper power supply. It could simply be that it has more capacitance or other features in the power supply to boost that rating. If in fact an inferior PS transformer is used, the 'dynamic headroom' is not going to get higher.
Now if you look at it another way, say:
Amp A - 200W cont., dynamic headroom (as defined by OP) 400W or 3 dB
Amp B - 250W cont., dynamic headroom (as defined by OP) 315W or 1 dB
Then we have a choice to make, and I would likely choose Amp B as I perceive it has a more robust power supply transformer, but if Amp B's cont rating is also only 200W, than Amp A would be my choice for the better headroom. YMMV.
I should emphasize that the NAD example I used may not be appropriate, without knowing how they define their dynamic rating, but for argument sake I am assuming it is for 200 ms or less.