Needless complexity.
This isn't a technical challenge, it's a usability one.
Sure the mechanical tooling could be adjusted to do that, and in some high end cell phone cameras you do see some truly bizarre shutter speeds to adapt to their limited range of aperture... but WHY? What technical advantage would it present you to be able to do 1/19th instead of 1/20th? I don't think anyone has made an argument for any case that sufficiently convinces camera makers that it's worth the added complexity.
The same goes for the aperture. If you go back to really really old cameras you'll see continuously variable apertures that could be adjusted to any value. But folks quickly tired of having to do the math to figure out their exposure and started marking spots on the aperture dial to stop the adjustment at that were uniform amounts of light apart. (Here's where we get the concept of an f-stop.) It was just easier to work in evenly spaced units than infinitely adjustable places in between.