Even with 2 sigma confidence lines there is barely a correlation in a lot of this data. If we looked at the 3 sigma confidence lines there would be nothing here.
I remember one study had such a small sample size that a single man having a heart attack on his way to work was the bulk of evidence used to criticize the time switch. A scientist with an agenda can usually get their position published even if it's questionable.
The overall evidence weakly suggests there are negative health effects here when we make a time switch. But if it was truly a large statistical shift with high confidence values then we probably would have a much stronger scientific case to address time shifts in our society cycles. We would also have to include a much wider study. Are there papers looking at the possible beneficial effects of these time switches out there? And lastly, is this even worth the research time and potential implementation cost?
As it stands now, it's basically just a bunch of people's personal preference of when they want more light relative to the standard work day. Personally I would be happy to use UTC worldwide and just shift the hours appropriately with location, but that won't fly with most people.