No, that doesn't hold. I'm not addressing that at all. For the previous commenter to be correct, the trend should start with the intervention, which occurred in/around 1900.
I've already hinted at why that's not a very strong prediction either. Sanitizing fairy tales are only one part of a broader trend toward sheltering children in general, which, to my knowledge at least, did not start at exactly the same time. The changes in mental health would track with the intensity of the broader trend, with a time lag of around 20 years. Yes, these are both very difficult to measure. Truth is hard.