Folks who want that sidewalk in front of their property may be required by the owner of the sidewalk to keep it clean.
In nearly every instance at one time or the other the owners of such sites have elected to have a public sidewalk, so that's become part of the deed description. I doubt you could actually remove the sidewalk and thereby get out of keeping it clean.
Here in Fairfax Virginia we used to have a law that PROHIBITED you from cleaning a public sidewalk. That was strictly the prorogative of the government!
Ah, so I guess it just depends on what city you live in then. I just couldn't imagine being responsible for shoveling every time it snowed! Thanks!