I don't know about this...

My first pair that cost more than $100 was the Beyerdynamic DT 770 250 ohms. Didn't have amps. Used it over 2 years just fine. Decided to upgrade to the DT 880 600ohms after discovering how much better it sounded but everything was too soft when I used it at home.

Decided to spend the minimal on an amp to see if it makes a difference and bought the O2 amp. Not only did the DT 880 sound exactly as good as I auditioned it, I discovered the DT 770 which I've listened to for 2 years without an amp and was super familiar with its sound and was totally fine with, sounded much much better with amps.

Tried a few more times with and without amps to make sure it wasn't some hallucination and bias and there's definitely a huge difference.

I became a convert in the efficacy of amps from then on. That's what made me plonk a considerable sum for an endgame amp ( the Drop THX 789). But I have to admit I couldn't tell there was much difference between my dingy O2 and the 789.

So I'll go so far as to say there could be some snake oiling when it comes to super high end amps but I still swear by the difference between any amp and no amp at all for high impedance headphones.

It's not really about adding bass and treble with an amp or making it louder, it's more like if you buy a really good and expensive pair of headphones, you can listen just fine without an amp but you're probably not going to hear all the detail the headphones is capable of producing without an amp.