It does not really matter to the person on foot what is private or public, or who owns or controls what, if the end result is a pleasant environment for people.

Let's blur the lines as we blend between a street, a covered street, an arcade, and a mall;

I love malls, unlike many urbanists. Perhaps it is because they provide a 100% human-oriented sanctuary from the hypertrophic environment outside;

The same can be said for suburban malls, because most malls are;

1. Fine grained. You have a vast number of destinations within walking distance.
2. 100% place. Space is highly utilized - there is very little exposed infrastructure or dedicated vehicular roadways taking up space or making you feel out of place.
3. Indoors. You are in a comfortable climate regardless of it is raining, shining, freezing, or blistering hot outdoors. (I was really grateful for this when I used to buy lunch everyday from a food court.)

There is no reason a city cannot provide all of the above. But, if that is the case, would a traditional city environment with plenty of covered fine grained narrow streets largely make urban malls obsolete?

America's best city planners are off building university campuses, amusement parks, zoos, and mega-malls.