New York, San Francisco, and Washington D.C. have significantly higher commute times (including by public transit) than less dense cities. New York's subway riders have it particularly bad, spending an average of 7.5 hours per week on the trains [0]. This is despite those cities having some of the best transit systems in the country [1].
I'm aware of the finding that lower commute times are associated with happiness, but that makes the opposite of your argument. The lowest commute times are found in small, low-density, car-oriented cities. Even in New York, drivers and taxi-riders have shorter commutes than public transit users.
As you'll see in the report, a very lucky few have short walks, but it is not at all the norm. I surmise that if you can afford to live within walking distance of work in New York, you're likely an order of magnitude too rich to need to work.
Your other points are valid, but I'm highly skeptical that these benefits are worth the extra $2000/mo they bring in housing costs (when collapsing a 3-bedroom house family into a 1-bedroom apartment), particularly when we are talking about people who do not have $2000/mo.
I say this as a relatively new Berkeley to SF public transit commuter. I love my job, but I'd rather stab my eyes out than spend 80 minutes on overstuffed, lurching BART trains every day for the rest of my life. Fortunately, the gruesome death vs. BART tradeoff is available in the form of motorcycling, which I'm trying next.
[0] http://origin-states.politico.com.s3-website-us-east-1.amazo...
[1] http://ao.umn.edu/research/america/transit/2014/index.html