Most modern prints are digital in origin. There are several units to consider.
First the file. As you know you can have different bit depths on a file. Current systems use 8 bits per channel (you already knew that).
There is an additional unit in the mix besides bit depth, LPI, this is, Lines per Inch. The amount of shades a plate can provide depends on the relation between the defined LPI and the DPI (Dots per Inch) the device can handle.
If you need 150 LPI, and your device can print 2400 DPI, then each line has at its disposal 16 linear dots (2400DPI/150LPI = 16 dots)
This means you have at your disposal a square grid of 256 potential combinations of dots to produce an LPI dot.
If you vary the relationship between the desired LPI and the DPI the printer is capable of, you can have a different amounts of shades any given grid can provide.
Any modern plate printer can give you around 3600 DPI, which means that you can push the LPI resolution to 200LPI (depending on other factors such as the type of paper you are using)
The Scale of 0-100% is due to historical reasons, before the digital era. But it gives you enough room to make a series of swatches. But if you are preparing a gradient, this gradient does not jump from 50% to 51% for example. It is translated on the background to its equivalent to, let's say an 8-bit scale. You can see this if you export the file to a raster image.
It is not necessary to use more values than a 0-100% scale, because the visual difference is so insignificant, and the printed result has so many additional variations that a small dot of those 256 possible dots is not a big deal.
The real dot size depends on the absorption of the paper, the gain, the pressure of the rolls, the humidity levels, ink density, etc. A tiny dot of the 256 available is not that important.
There are some additional elements to consider. The grid I am showing is not as direct in real life, because these grids and halftones are rotated, so the final dots used on each grid vary. Also, you have the shape of the "circle" that can be an ellipse, a diamond, etc.
But is, IMHO a good explanation to understand the number of shades on a print.
You can also have the scholastic method to produce shades, this is similar to the one used on an inkjet printer, using an error diffusion to distribute the dots to produce shades.