>>106327840
>Every circuit suffers from some level of noise
None of this matters, noise doesn't somehow suddenly make the signal have discrete levels. The noise averages out over time. 0.01 +- 0.05 is still observably distinct from 0.02 +- 0.05, given enough time. Your eye has more noise than the tube either way!
>No PC from 20+ years ago when CRTs were in use ran any video mode beyond 8bpc sRGB
Just plain WRONG
https://www.tomshardware.com/reviews/opengl-workstation-power,334-17.html
2001, Wildcat II 5110, features a RAMDAC with 10-bits per color channel.

But either way, with CRTs all you need to do is upgrade your RAMDAC, was it your GPU or an adapter, and you can increase your bit depth. Unlike modern planned obsolescence garbage, tubes kept benefiting from advances around them.