I would say your general point is correct, that since the amp resulted in this difference in balance, it is a significantly better experience. Being unable to play the headphones at sufficient volume, either at all or else without audible performance degradation, is a serious impediment to the overall performance of the system. What I'm arguing is that people might be attributing the improvement they hear in properly amping their headphones solely to the amp, as though there were some intrinsic property of the amp itself that caused the effect. In fact, assuming my hypothesis is correct, a large part of the improvement comes much further down the signal chain, in the listener's own ears.
It's largely an issue of semantics, except that it also predicts your other point, that the difference between a $1,500 amp and a $5,000 one shouldn't be tremendous, since the improvement that comes from properly powering the headphones is already sunk--both amps will produce sufficient clean power for the headphone to reach the desired listening amplitude. Any difference in performance, then, will come down to differences in design, and this will probably be a lot more subtle (unless there's some kind of electrical mismatch between the headphone and the amp).
The main point I'm getting at with all this is that a lot of people express the belief that the initial level of improvement they get from properly amping (and therefore being able to reach desired volume without noticeable performance loss) will continue to be realized each time they upgrade. I'm sort of throwing out the idea that this initial improvement is something you'll hear with any amp that has the chops to power your cans, and that any additional theoretical improvement from upgrading to an even more expensive amp isn't going to be of the same nature or magnitude.
Thanks for the thoughtful reply, I love the 880 thread, always so chill and with plenty of great information. I like how you illustrated the intrinsic difference between two capable amps as mostly being "sunk", and the point of diminishing return being perhaps quickly past as you climb up the amplification food chain.