This would be ruinous. Yes, it'd be great if we could compact and leave most of America pristine, but that's not what would happen. Leave all that open space and people will expand into it again, except likely as much more dense populations.
This would result in mind bogglingly large population growth, which Earth can't take right now. We need LESS dense populous, not more.
Are you saying that we would have increased population growth if the population was all packed together? By packing together we could do things such as use less electricity by being more efficient (less power loss due to transmission distances, less power used to pump water all over the place, less fuel spent moving all over the place, etc).
If we concentrated the population, we would not grow as fast. But that all depends on concentrating the population and then not allowing it to expand beyond some set borders, which doesn't seem like it'd go over well. Just look at the little countries running out of land, looking to their neighboor's turf as prospective expansion.
You'd need government or fences or armed forces preventing people from expanding- it is natural for people to expand.
Maybe I am incorrect in thinking so, but my idea was that while the birth rate may be lower, we'd (in the end) approach a higher net population density if we slowly sprawled from a single super-dense hub.
Brooklyn has obviously grown since it was created. The creep, as I understand it, is generally just as population-dense. That is the effect I am talking about.
This would result in mind bogglingly large population growth, which Earth can't take right now. We need LESS dense populous, not more.