Actually, the Barnes Dance is not new at all, merely forgotten. It was installed fairly widely in New York City decades ago by traffic commissioner Henry Barnes. He borrowed it from even earlier usage. When he stepped down, the Barnes Dance pretty much departed with him. IMO one factor was that traffic engineers loathe anything unfamiliar. Extreme conservatism is par for the course in safety-related occupations, as, if you change anything even a tiny bit, then you are to blame for all future deaths and injuries, even if they are fewer in number, and even if the ones that still happen would have happened anyway. That's all the more true in the famously, or rather infamously, litigious USA.

In addition, periodically shutting down intersections altogether to cars reduces traffic throughput. At standard intersections with standard signals, straight-through traffic is moving along one of the two available axes essentially all the time; at Barnes Dance intersections it is not. Since Manhattan is a place where crosstown traffic moves at about 1mph for much of the day, anything that even gives the appearance of impeding traffic (especially weekday traffic) may prove to be political or legal suicide.

After all, even in a place that crowded, it's not practical or equitable to force absolutely everyone to walk. They may be physically unable, they may need to be bringing luggage along, etc. I do suspect that TOD posters (and Web users in general) tend to be: disproportionately young and thus more likely to still be physically able; childless and lugging along neither kids nor all that kid stuff; and recently steeped in nihilistic academic postmodernism. Any of those and other lifestyle and ideological factors, even operating alone, may blind them to some of the reasons why others might use cars.