Headphone amps do sound different

Most of you will say Duh. But I keep buying more and more expensive headphones trying to get a better sound. Brought a Grado 125, then to a mid-price Audize, then to Grado 1000. Improvements, but still not there. For other reasons not related to headphones, I upgraded to a Class A integrated. When I did finally plug in my Grado 1000’s - there it was. Magic! The sound was clear, open and musical, like a Wet blanket removed. The soundstage was so wide it was as if I was not even wearing headphones at times.

So, that’s my story, I’m sticking to it. Please, no one tell me about some separate headphone amp that will improve it even more.....