From TFA: “ There isn’t likely to be any danger in listening to BROWN NOISE for, say, eight hours at a time, Dr. Berlau said, unless someone plays the sound at unsafe volumes (listening to noise above 70 decibels over a long period of time can damage your hearing).”
The only consequence I can think of is that you might find it harder to go to sleep without them for a while. That was my experience with always using a mechanical background noise generator throughout my childhood, and then not.
It's like a fan in an enclosure with adjustable vents. It's louder than a fan of equivalent size. They've mostly been replaced by electronic background noise generators these days.