Few places in the world are as poor in terms of lack of public spaces as the US. Roadside cafes, town squares, etc. are the norm in Europe. In the US, very few cities have such features. They are increasingly common these days in the form of 'suburban town squares', but they are almost always in some shopping mall or similar commercial enterprise, rather than in truly public spaces. To further complicate matters, even in college towns, faculty and researchers prefer driving to work than riding public transport. Nowhere is this more common than in the American Midwest, with its combination of vast sprawls and severe winters.
Maybe it doesn't matter in theory, but in practice they're usually really different. Public spaces tend to emphasize nature more, and tend to be larger and quieter - an ideal environment for relaxing and letting the mind stretch out. Parks don't have an agenda. Commercial spaces typically are small, loud, and filled with kids. They're designed to be more about resting in between commercial activity.
Noise and context. Mindset. The mall is a place where people go shopping - quick in, quick out, everyone is moving; lots of people in a closed space makes constant noise. It's not a place you go to to slow down and relax.
Whereas a park, and a café near it, are usually much more quiet, slow-going. People expect to be able to slow down and relax. In a café, there is no constant flow of customers, so the owner doesn't have the incentive to kick you out as soon as possible.
Doesn't matter too much. Only problem is that it exists only so long as the mall developer is making a profit on the space. This is hardly true with say, the cultural districts of cities, where taxpayers foot the bill, and where there is intrinsic real estate value. Many cities have been successful with the latter model, Pittsburgh comes to mind- with its very town-square-ish Southside and Portland's Pearl District- both urban rejuvenation projects which did not involve converting the whole place into a massive mall.
