Of course not. Unless you're willing to remove the usage-based taxes for motor vehicles too and fund those the same way.  It's the unequal treatment that's the problem.

As a general rule, I favor usage-based taxes where they're reasonable to implement.  Which they are on motor vehicles, and on bikes (as something like a special sales tax).  Could that be extended to sidewalks, city parks, etc for pedestrians?  I don't see how from an implementation standpoint since usage of those isn't typically tied to a vehicle.  If you can think of a reasonable way to do it, I'd be opening to hear it, but I can't think of one off the top of my head.  But for vehicles (motorized or bikes), yes, there are reasonable methods.  

(And FWIW, many parks do charge a usage (entrance) fee, like national parks, so there is some precedent for that too.  And I think in Denver, sidewalks are often paid for by the property owner.)