I honestly do not know. They definitely do for still photos—Nikon has had chromatic aberration correction and lens distortion correction for quite a while, and it’s keyed to individual lenses.
If they aren’t doing that in video, I suspect it’s a pure horsepower limitation. Reading the data off the sensor, and applying the corrections in real-time while writing to card may be too computationally intensive or bandwidth-limited.
https://www.sony-mea.com/en/electronics/support/articles/000...
Pretty much this, and this is what some people already do with pancake lenses, correcting the result in post. However there's a problem with this: for the universal vendor-supplied profiles to work well, the lens must still be made within pretty tight tolerances, so the cost reduction is limited. And proper manual calibration is really expensive and tedious, which defeats the point.
I don't know if there's a niche, but I'd love to see some startup doing the full-fledged lens and body calibration (STF/OTF and stuff) on demand to make high quality custom tailored profiles. That way you can use really cheap and compact lenses to get the same result; software correction can do wonders nowadays.