This is the weirdest application of Friedman's plucking model I've ever seen. Friedman did not show deep recessions can't have slow recoveries, he showed that the magnitude of the recovery is correlated with the magnitude of the crash and not vice versa (which is an argument against "cycle theories" where the reverse is true).
And as far as I know no one claims that deep recessions have to have slow recoveries (what Taylor claims Friedman demonstrated was false). What they claim is that recessions caused by financial crises are both deep and have slow recoveries. In the past when Taylor has made this point he's qualified that it's worse than other cases with financial crises - that may be true but it's quite different from what he's saying here.
Notice also the metric that he use (change in the employment to population ratio). It's not a bad thing to think about but it's worth looking at the long-run evolution of that metric. We were facing E/P headwinds before the Great Recession because the increase in female labor force participation was petering off and because of the aging population (the situation was very different on both fronts in the 80s). So it's a little misleading to compare the two periods on this metric.