I don't understand the sidewalk accuracy argument.
With street width, the sidewalk location can accurately computed, no?

In theory, yes. In theoretical practice though, this would require that the street width would be tagged accurate at every running meter of the street and errors in that width would add up with errors in the street's position, so drawing the sidewalk separately from, aerial imagery might be more precise. In actual practice, the offsets in aerial imagery and noise/error in GPS positions tend to be much larger than this and the navigation way's topology tend to be much more important than the precise location of the ways.

So yes, if you're worried about sidewalk location, and the sidewalk isn't physically (by space or barrier) separated from the street, do tag street width or at least the number of lanes and make sure the street's way has a reasonable location. Only where the sidewalk is physically separated draw them as separate ways as precise as feasible and make sure you connect them properly to the streets where the separation ends or is broken (gates in barriers, road intersections, pedestrian crosswalks, asphalted gaps in the space between road and sidewalk, ...) so that navigation can work properly.

Unfortunately, the "Sidewalks" article on the wiki doesn't currently mandate that convention, merely hints at it, and I'm not sure whether there's strongly enough consensus to change that document accordingly. (See also this old (2012) discussion on that article's discussion page.)

Regards,
Raphael