There are so many really cool looking pump action shotguns available but no modern looking 22's.
"Cool" is in the eye of the beholder. I think my Winchester Model 62A is pretty cool.
If you want "modern", why not just get something like a Ruger SR22? Pump action .22s are a technology that has largely been superseded by semi-autos. Asking why there are no modern-looking pump .22s is like asking why there are no modern-looking slide rules or Curta calculators. Those that like 'em, like 'em precisely because they're old-fashioned.