No they don't!
When audiophiles are in the market for a new amp, they usually look to get something that will be able to handle at least 115dB SPL into whatever transducer they plan to use with it. they do that because there is almost no situation that could require more. For the er4sr 115dB SPL that's about 11mW into 45ohm at 1kHz. POWER!!!!!!!!!
While you can find a few old devices(at least 1 or 2 Sony DAPs) that can't even get 11mW per channel into that load, such stupid devices are hard to find nowadays. Almost any audio device, cellphone, portable amp you can purchase will handle 11mW into 45ohm like it's nothing.
And that's the power to get 115dB SPL at 1kHz. With Ety, 3kHz is going to be like 10dB louder. Who wants to listen to music with 125dB peaks? Not me. Most people will use their devices to listen at levels that will massively reduce the actual power flowing into the IEM. On my DAP, set as I just used this afternoon with the er4sr, I land an impressive 0.13mW(yes, milliwatt) at 1kHz. And again it's 45ohm, not a difficult load at all. Most portable devices will have a perfectly fine damping ratio into this. So maybe you can understand why my head blows up when I read your post trying to emphasize power for that IEM? Because it's crazy.
If you mean something like keeping the signal linear thanks to good damping, stable amp output or whatever idea like that, the correlation you're looking to establish is probably about distortions instead of power. If you think about noise, say noise. If you have no idea what's actually causing your subjective impressions, say that. Most people don't know jack crap about electricity or other objective audio stuff, and they live very well that way. Or IDK, say how in your opinion better devices are better. We won't be learning much but at least it's a statement I can stand behind.