The main reason behind this train of thought was that they thought that blindfold chess may contribute to going crazy. They looked at Morphy and Pillsbury as their primary examples. Lasker, specifically, thought that blindfold chess made Pillsbury go mad, but we now know it was syphilis. Other than just plain incorrect assumptions like Lasker's, this is an incredibly small sample size no matter how you cut it, and we are talking about judging this on 90+-year-old "science", if you can call it that.
This not only does not make any sense in the modern day, but it has been debunked by at least USCF NM, and noted psychologist, Christopher Chabris from Harvard. The paper can be found here.
Blindfold chess is good for your chess vision, so feel free to practice it in moderation.
P.S. We have in more recent times, from 1992-2011, had the Melody Amber blindfold tournaments for the the top players in the world including Karpov, Kramnik, Anand, and Carlsen. If modern science even remotely believed that blindfold was bad for you, these guys would not have played.