how, I don't see how, access=private tells you who is allowed on a way while *=designated tells you the type of transportation allowed on a way not who is allowed on a way, removing bicycle=designated and foot=designated would remove important information in this case. access=private tells you only certain people can access this way while bicycle=designated + foot=designated tells you that only bikes and pedestrians on foot are allowed to use these ways. the *=designated tags don't say that anyone can use the way they imply no such thing, they just tell you the type of transportation allowed on the way and in that way doesn't override the access=private.