When iOS was first released everybody and his dog was still running their own proprietary movie (container) format. Microsoft was pushing .wmv, websites used Flash, illegal sources were using .avi files.

Apple forced these sites to provide their streams in a standardized format, MP4.

It might not be the standard you want because it isn't patent free but at least it is a standard, it's not controlled by Apple and it works on just about any device and works pretty well.

I have VLC installed and Messages refused to save/play .ogg's even though it shows up with a VLC cone (including 3D touch "hard press" menu).

That's a completely reasonable thing to do, especially because it might allow you to pick up distortion due to interpolation.

However, you should do the same thing to the white noise [1] if you are going to compare them. If we write the white noise's continuous reconstruction [2] as a function of time, w(t), we could stretch out w(t) until it wiggles at about the same rate as the perlin noise, p(t), and then sample them together at a rate several times higher than that at which they wiggle. Both waveforms would then have the same "muffled roar" sound you get in airplanes, buildings, underwater, etc.

Another mundane explanation for the bands is that they might be "JPEG artifacts" for ogg's compression. Amplitude is logarithmic, so they're probably not as important as they look.

[1] To be pedantic we should call it band-limited white noise, because the sampling+reconstruction process limits the bandwidth, and infinite bandwidth white noise can't actually exist, because it has finite energy per bandwidth * infinite bandwidth = infinite energy. This isn't a theoretical problem. Oscilloscopes have fatter "no-signal" traces in proportion to their bandwidth, the resolution bandwidth ("RBW") of spectrum analyzers lifts the noise floor at higher settings, the field of thermodynamics fell apart in the "ultraviolet catastrophe" before we understood how quantum mechanics effectively limits the bandwidth of thermal radiation, etc.

[2] w(float t) rather than w(int n), obtained by interpolation. Sinx/x interpolation is the interpolation that gives 0 distortion and produces no higher spectral content. It's the time domain equivalent of doing a Fourier Transform, scaling the spectrum, and doing an Inverse Fourier Transform. IIRC Perlin noise is a spline, not sinx/x, so I'd expect its interpolation to produce higher harmonics. By applying perlin-like (spline?) interpolation and sinx/x interpolation to the white noise, you could isolate the audio effects due to the randomization vs the interpolation of the perlin noise. If you were so inclined :)

IIRC there's some evidence that very low-frequency sounds may cause feelings of anxiety and fear in human subjects. Very low frequency sounds may occur prior to catastrophic events like earthquakes, and some animals have been known to react to it. It's plausible that humans have evolved a similar protection mechanism which has gradually atrophied. That being said, I'm talking about sub-20 Hz frequencies here. I don't think these recordings contain that and I don't think it would be possible to reproduce on regular headphones anyway...

Constant, uniform stimuli for extended periods of time can produce weird effects on the mind. Think about stuff like sensory deprivation, staring at oneself in a mirror, anechoic chambers... And if someone can find a given sound soothing it's not out of this world to think that another sound could have the opposite effect.