I've wondered about that myself, sometimes - there's another web of these ways near the visitor centre at Ham Lane.

Rob Whittaker (who put this one in) is a veteran mapper, though, and I think worth checking with him his rationale for using highway=pedestrian. If data consumers / checkers are flagging this as an issue that may be a false positive: I can't see any clear rationale why a highway=pedestrian must have a name, where a highway=footway need not; and simply by what's on the ground I can see why these are said to be more than a mere "footpath" (=footway's natural language translation)