"My method is to use Photoshop and use the saturation control- reduce down the color until it is nearly B&W-- but it's STILL a color RGB image. This looks much better!"

Agreed, it may look better... but it's still not a B/W image. It wouldn't look right printed on a B/W-only printer (if such a thing still exists)....

The vast majority (currently) of apps, formats, VDUs and (home-owner) printers support the 32-bit paradigm:
8 bits for each of the R/G/B values (=24 bits) with 8 bits left over (usually either unused or used for alpha-mask info). That means that each of the R/G/B channels can vary from 0-255.

Since (true) grey-scale means that R = G = B for each pixel/dot, then there are (as said in Impish's post) 256 levels of grey available. Not the best by any means, but the best that most of us poor home-owners are likely to get for some time to come.

What WOULD be nice is a totally new format which used (eg) 16 bits/pixel specifically for grey-scale images. But that would require changes to the majority of software/hardware for what is rather a niche market these days...I'll not hold my breath, nor save up my pennies (pennies wouldn't be enough..)

Cheers,
Diolma