I'll agree and disagree, and try to explain
I'll agree because I've heard exactly what you're describing with my stereo speakers. I switched between two amplifiers, made by the same manufacturer mind you! The new amplifier was spec'd to 170 watts per channel, which was higher than the amplifier I had been using (probably 120 watts). The new amp was also in a more convenient package. But I listened and listened and started to lose my mind, until I realized that the sound had changed dramatically. Switching back to the original "lesser" amplifier, the soundstage returned. The same thing happened when switching from what I would call a "standard" DAC (i.e. Schiit Bifrost w/ Uber, Oppo BDP-105) to a Meridian Director. Think what you will of the proprietary processing that Meridian runs, with no options to turn off - the soundstage again grew wider, taller, deeper, whatever adjectives you would use to describe it.
I too have heard soundstage when a specific DAC/AMP is paired with a specific headphone. But to my ears, it is not to say that because DAC/AMP model A works well with headphones B, that it will also work well with headphones A and C. It just doesn't sound that way to me. What created a vast, amazing stage for me with one headphone will often fall flat with the next headphone, despite IMHO the next headphone having a generally larger soundstage. So that's why I tend not to try to focus on soundstage when speaking of headphones and DAC/AMP products. It may be a magical pairing, or not
Just my thoughts