I don't think the goal here is to increase density, but to "provide affordable housing". High-rises tend to fail at that, to judge by the experience of the US "projects" and UK "estates", precisely because of the lack of services and open spaces. When the capital development of a country becomes a by-product of the activities of a casino, the job is likely to be ill-done. — John M. Keynes
That said, there's already a severe street-parking shortage near my office, and they're currently building two more highrises across the street; it looks like at least one of the buildings, if not both, are ignoring the city's requirement to build parking in any new construction, so we're bracing for a nightmare if and when those buildings are actually occupied. (Which, the way things go here, could be years after they're actually built.)
Washington D.C. also has a height restriction, as do some of the surrounding communities; this blogger based in the Maryland suburbs has some interesting suggestions for regulating the construction of taller buildings so as to make them greener and more workable.
NYC has strict parking space laws that work in the opposite direction in Manhattan - i.e. you are not allowed to build much of it. That's a good thing - the core of the Midtown office district has about 700,000 jobs packed into one square kilometer, I'm not quite sure how one would handle that with car based commuting.
Lack of parking space has been shown to be the single most important factor driving traffic in Paris, so the city is busy reducing the overall stock inside Paris. In the long run, we're all dead. John Maynard Keynes
Also, what is really critical is indeed to avoid the lack of services (open spaces are present in French projects, and are mostly misused ; also, towers in Paris would be within an urban environment, unlike the projects in the suburbs which suffer of exclusion from the rest of the city).
Also, the goal may be to provide "affordable housing", but the target isn't the poor, but rather the middle class (people like me) who can't afford Paris any more. The social problem this potentially causes are quite different... Un roi sans divertissement est un homme plein de misères
I don't know the number of 8+ story buildings in NYC, but given that there are over 5600 12+ story ones within the city limits I'd beg to differ. (Paris has less than 500 - not completely comparable, a much smaller land area, on the other hand the outer parts of the outer boroughs are generally zoned low rise or even single family in some cases)
Also, you have to make sure you have enough services and open spaces in the vicinity.
The services aren't a problem. Open spaces, well thanks to some nice city planning over a century ago NYC does fine on that count, but it isn't easy to reverse engineer into a different layout.
More seriously, there already are some high-rise housing neighbourhood in the outer arrondissements of Paris, and they are not unlivable. Both need to be done : density increase within and out of Paris. Un roi sans divertissement est un homme plein de misères
