I think that we have a privileged view of this question in Epidemiology. None of the professors who were being hired when I started my PhD had ever done a post-doctoral fellowship (as other than a one year stint to get another university on their CV; only about 50% of them had done even that).
Now I am entering the second year of a post-doctoral fellowship and you can see the change where it is becoming common to do a multi-year fellowship. Although, I still see cases of people being hired into faculty directly out of the PhD or, more commonly, trying to be hired as faculty directly out of their PhD program.
So this makes me sympathetic to this post by MsPhd. It being widely panned elsewhere, but I wonder if the main point is being missed. Post-doctoral training is an ideal phase for "creep" in expectations. It's pretty clear that standards are rising in biomedicine for what it takes to succeed. Some of this is good -- a solid arms race will produce better outcomes. But the dark side of this process is people being kept back for very long periods of time. If this process leads to happy outcomes (or decent outcomes) for all involved than this is perfectly fine.
But what if it doesn't?
What is the ideal length of a fellowship training period? My field's traditional answer of "none" seems too short but more than five years seems too long. Or am I missing something?