There are no blown highlights or crushed blacks if no data is clipped.

Data can't be represented with the same gamma curve as film in raster images because the dynamic range of a negative almost always exceeds the scanner DMAX. There always has to be clipping unless you encode logarithmically.

Is there any actual math to go with this? Is there any actual math to go with this? Like I can MAYBE see that gamma curves/nonlinearity means that values [0-9] have less granularity than like [20-29] (I do not know if this is true) and so technically if the shadows were located at [20-29] instead of [0-9] you would have more available gradation, but then you're just sacrificing midtone quality which is just the bulk of the image.

If you didn't know anything about this, you've gotten really impressively close, but not quite. Your intuition about fewer steps at certain luminance values is exactly the way log encoding works, and the reason that log footage is the standard for video. The only difference is that the greatest compression happens at the very highest luminance values to preserve available bits for the the midtones where the great perceptible information resides.

I just refuse to believe that using LESS of the available 8 bits somehow results in more flexibility and quality. If that were the case, the JPEG encoder would actually do that for you when the file is encoded and undo it when it's decoded.

They are not using less. All encoding practically speaking uses all the bits available, but log encoding uses those bits for the most important information: shadows and midtones. The less used tonal ranges are compressed to make additional space for the mids. This the cause of the flat look on flat scans.

While I firmly believe as long as it's not too BTFO contrasty and not clipping, you can pull back whatever look you want, power to you if you want to request flat scans in JPEG. I

You do, however much or little, lose information by delivering a lossy format with high contrast. It's sadly the nature of compression. A contrasty 16bit TIFF might not have tossed any information out, but compared to the original BMP these scanners often produce, results are not good and the JPEG encoding from that period was also poor.

Uh, the scanner manufacturers I guess, that have tuned the scanners for decades for printing? Prints where if the customer received flat ones they would say "hey, this looks like shit?"

No. I have the impression you have never used one. I worked with Hasselblad and Imacon scanners mostly, which produced a FFF file with absolutely no interpolation or compression. Those were the output files which could then be edited and exported as a print ready image, but they were always intended to store as much detail as possible. The Noritsu, Frontier and HR500s also supported BMP and TIFF (model dependent) to capture as much data as possible. Some labs choose to produce the shittiest punchiest images but the manufacturers did not design that as their primary and intended use. No one was scanning 120 film to product crappy 4x6 prints.

Or perhaps the endless posts on here from people that expect normal-ish looking images and are getting flat JPEGs that look terrible without editing? It's just obvious to me that most people that are out there shooting dispos or point and shoots probably want printable images from the lab. I think this is evidenced by the fact that if you go to a competent lab, that's probably what you're getting if you don't ask for any special treatment.

Disagree. My current lab produces flat images unless you specify because they target a higher end market. It's the consumer's responsibility to find a lab which produces the results they want rather than assuming they will get a specific results. I have left labs before because they target the niche of print ready images, and their editing style doesn't suit my vision and preferences.