wall of words!!!!
So, what are some amp+phone pairings where you notice the problem? Something affordable, perhaps ;p
which problem? if you're talking about the frequency response change that could be caused by using an amplifier of different impedance output, then many IEM can change audibly simply by going from maybe 0.5ohm to a 2ohm amp section. typically multidriver IEMs where you have the impedance curve going from very low impedance to pretty high or the other way around, or even have several back and forth due to crossovers.
you can see some examples of using the same IEM on amps with different impedance in my post here
https://www.head-fi.org/threads/feedback-about-gears-stop-doing-it-wrong-impedance.866714/
my JH13 aren't the worst and you see that you need pretty substantial impedance output to make a relevant change in signature. but if you were to check the same impact on IEMs that go as low as 4 or 5ohm at certain frequencies, like the Shure SE846, then the variations would be much bigger and even a few ohm would be audible as a frequency response change.
for headphones, on my HD650 the impedance curve has a pretty serious bump around 100Hz. so when you use a high impedance amp, you can see measure that area being boosted a little. but as the lowest that headphone ever reaches is already several hundred ohm, you won't get a big bass bump by switching a 0.5ohm amp with a 3ohm one. because both already offer more than enough when it comes to damping ratio, ensuring minimal change in frequency response.
so it really depends on the impedance curve of the headphone/IEM when they become part of the complete circuit. but low impedance headphones/IEMs automatically are more likely to be more affected because it's about damping ratio.
two warnings:
- here I'm specifically focusing on headphone's frequency response variations due to impedance. in reality there could be other differences aside from FR, and even for FR, other causes could affect it. different amps may be different in many ways.
- we're often assuming that the best damping and amps with lowest impedance are best, but subjectively you might find situations where you'll just prefer the sound from a higher impedance amp.
Perhaps there is a special high impedance headphone cable you could use, in place of a high output impedance amp? (Assuming detachable cable feature)
we can do that of course, adding one resistor to each channel, or even creating a little voltage divider. but you have to remember that it's "seen" as a change for both the amp and the headphone. the amplifier "sees" the headphone+cable as the load, while the headphone "sees" the amp+cable as the source's impedance. so by adding a resistor in series, you will worsen the damping ratio, while reducing the volume level(that the amp will have to be able to compensate). once again, it's a case by case thing to consider, but overall, it's not the answer IMO.
when it could be good:
- if your amplifier simply can't handle the current flow because your IEM has too low an impedance, by adding a resistor you reduce the current flow and could help the amp work nominally again despite still using that IEM. you'd just have to check that the possible change in signature doesn't displease you. but that's a pretty extreme situation, usually such a thing just doesn't happen unless the headphone has both stupidly low impedance and low sensitivity. a few planars or something like that maybe, but usually when you have such difficult headphone to drive, you know about it and get the amp for that specific job. I'm only listing what could exist, not saying that it's the norm.
- when you simply like the sound better with extra resistance. the most famous example of this would be the Etymotic ER4. the ER4S that the vast majority of users prefer to the ER4, is an ER4 with 2 75ohm resistors in the cable(one per side). it reduces the entire listening level, but because of the impedance curve of the ER4, the attenuation is slightly bigger in the low and mid range compared to the trebles. so once you've finished matching the volume back to your preferred listening level, the trebles are slightly louder and Ety fans usually like that.
- another use that has nothing to do with impedance, is to simply reduce the listening level with the hope to also reduce background noise. and hopefully when you increase the gain on your amp, that noise won't increase back with the music.
so once again, different circumstances create different needs/choices.
Is it dangerous to the headphones operate with such a mismatch..?
no.