I would argue that it wasn't the split within Superman's fanbase that resulted in Batman's rise to ascendency, but rather Superman's boy scout persona just didn't fit the mold of the new era of gritty superheroes.
The mid 80's to mid 90's saw a shift in comics towards more serious storylines, and a lot of adult themed violence in comics, this was primarily kicked off by Frank Miller's Dark Knight, Batman rode the wave of that popularity and never looked back.
Thankfully that era is over, but it's legacy can be seen in April's comic sales that point to all things Batman. Sadly Superman titles don't even crack the top 50.
https://www.comichron.com/monthlycom...1/2021-04.html