Yeah, transistor amps might be not a good fit for those cans, I would agree to that. I never heard a true tube amp, so can't say anything about that.
As far as i know, burn-in has been tested many times, and while many headphones don't sound different at all, some has slightly changed in the frequency response, but that difference is so little, that it's pretty hard to hear, as our human ears are not as good as instruments. What we hear after burn-in are our expectations.
In my opinion, everyone needs to ask themself, who has claimed this and what is the reason behind this? A company selling headphones fear that one may send it back, but when burn-in is in the play, many people expect for it to sound different and view it differently in search of something else and most certainly will find it, even when it was there before, they just didn't pay attention to that and realize it too late to send it back, because the playtime is over.
It's called confirmation bias and the reason, why often things in high price range won't be sand back right away. Where the burn-in really starts to happen is not the headphone, but we humans adjusting to the new sound over time.
I can compare level-matched DAC/AMPs if I want fair and square because I have a switch box and self-made cables for that. But graphs from headphones won't personally help me at all, because this is, for many reasons, a very subjective thing haha (hearing capability, ear form, genre, experience how instruments sound in real life).
That is my opinion on this. I hope no one got angry because of this post, if yes, I'm sorry for that, didn't mean to
EDIT: As a reference. I remember sitting in a conference room, where we had to be quiet for some time and the pc noise was driving me nuts, which is why I asked if the tutor could please put something between that pc and us, but no one could hear that, until a distance of 50cm, while I was sitting 4m away. Might be the reason, why I'm a bit sensitive.