In North American cities, there's a clear low density issue at play. Most of the previously dense urban cores were completely hollowed out to make room for roads, highways or parking lots. One can argue that the current reluctance to the pulling down and rebuild mindset is a direct consequence of the misguided development policies of the post war era. So much damage was done—and continues to be done—that people get very cynical of large scale development/infrastructure projects.
Whereas big European cities like Paris are very dense already. Maybe we could make them even denser, but I think at some point you start getting into negative return territory. I'd personally hate to see a bunch of magnificent 7 floors Parisian buildings getting torn down just to build sky scrapers. (Note: Sky scrapers are cool—but I don't think they are a scalable solution to housing, and by nature tend to require big developer involvement with political connections which then lead to perverse incentives—my personal preference would be to have a lot of smaller developers working on a lot of medium density projects, rather than very tiny number of big developers with very large pockets working on very few projects).
The focus should instead be on bringing areas surrounding the old city limits to the same level of density than the city proper—which is actually starting to happen in Western Europe now that we're starting to roll back some of the car centric policies of the past.