Which leads me to believe that that's just something that some headphones do when you try to get substantially more bass out of them than they were designed for. Is this kind of behavior really completely out of the question with working hardware and software?
The thing is if it was the driver ie the EQ is clipping and causing driver distortion, the driver will not suddenly make everything else soften just to try to reproduce those dynamic bass notes. A driver is a "dumb" part, and for the most part, so is the amp (I mean outside of temp/stability or turn on thump protections etc) that cannot selectively do that.
Like...while I may make the analogy that the amp output stage and power supply are like an engine and the preamp is like the transmission, you can't just equate transducers (ie audio drivers) to tyres/wheels on modern cars for one reason: sometimes the analogy is the road/traction is output impedance to load impedance, or in a more specific example to the problem you're having, modern cars have AWD and traction control. Amps and transducers don't have anything like this other than, say, crossover on a speaker deciding which transducer gets what frequencies, but ultimately when a high dynamic range note comes in it can't mute the other sounds in a manner like how AWD with TorSen limited slip differentials on both axles sends all the engine torque to just one side or just one wheel that it senses has the most traction (like the outer wheels when you're cornering, and front-rear distribution is affected by the weight distribution and angle the chassis is at).
There is however one other possibility: maybe we don't completely understand each other on what's happening based on your description. Maybe it
is clipping, hence the need for more power, but it's not so much that everything else is softer but that everything is softer. Including that bass note, except it's louder compared to everything else but could be even louder if it was getting enough power.
I've ordered a $40 portable amplifier because it annoys me that I don't know what's happening, but I don't have anything that supports balanced output so I can't test that sadly.
If your amp is single ended then it will only take single ended input, which a three prong plug can deliver from the phone to the amp. Not ideal as I would personally use a DAC-HPamp (regardless of whether it's SE or balanced; so long as it doesn't rely on bus power from the USB port) so the transmission of the audio signal will be from the smartphone's CPU as digital audio going into the DAC stage. But if it's just for testing if it might be power, then I guess not having to deal with a DAC-HPamp that may not work can be a temporary solution.
As for balanced drive...you'll have to check the phone and amp specs. If either outputs balanced then if your headphones/IEMs have removable cables then all you need to do is get the right kind of cable. But balanced drive on the phone is practically unheard of that even Quad DAC doesn't work that way the same way a dual mono DAC to HP amp circuit does.
This has been an issue ever since I got them, so yeah, same thing happens if I stream from Spotify or YouTube, or if I use other files.
Might be a hardware problem, and also that the description isn't what it seems to be ie not a software problem.
