Take a look at Downtown Toronto. Sidewalks are everywhere, paralleling roads or not, with or without separation. By your logic, every single one of those should be deleted for being "redundant". Deleting these sidewalks is a loss of information for no good reason. 

In hindsight, i probably shouldn't have linked the second wiki link, given it has a "dubious information" disclaimer at the top. It at least provides info that there are <1,000 instances of sidewalks being applied to the roadway as opposed to the >5,000,000 instances of separated sidewalks. I think that difference in numbers should more then justify separate sidewalks.