I can't say that's been the case for me.
I have a Stax SR-Lambda (with rebuilt drivers, admittedly) that I've been fond of, but I wasn't expecting to prefer it outright to the SR-202 and SR-303, which certainly cost more than their Normal bias grandfather does on the used market these days. They sounded different-kind of like the HE-400, in hindsight-but not better. Especially not in the midrange, which I prioritize most.
It could be that I'm just used to that old Lambda's way of presenting sound, but it does vocals in a way I've heard no other headphone do; it really seems like the vocalist is actually there, singing to you, totally natural and all. It doesn't seem like there's this raspy texture all over their voices that shatters the illusion, which has happened with many of the other higher-end headphones I've listened to.
How much of an expensive headphone's sound is expectation bias based on the price and its reputation, anyway?
Regardless, you may find that what you want out of a headphone isn't necessarily what the more expensive models are going to give you. Cost doesn't equal value to your ears.
Not all the time and not in every case. Take LCD-2 vs. LCD-3 comparison above IMO.
I don't know the prices of Stax headphones. So the SR-202 and the SR-203 cost 2X more than the SR Lambda?