I don't ever remember finding a Schwinn after going to someone's home who claimed they had "an old Schwinn" for sale.
It's name recognition. Same reason people ask for a Coke or Kleenex when they wand a soda or tissue.
Schwinn's marketing program was ubiquitous and they actually outsold many of the other brands, so for those like me who want a "bike like they had as a kid," Schwinn usually wins.
I'm a perfect example as I had a Phantom and a Tornado, but no Columbias.