Does everybody need reading glasses eventually, or do some folks never have this problem?

Mostly. All people have a stiffening of the natural lens from ages 40-55. If they never wore glasses, they will need reading glasses in this period and beyond. If they need a distance correction, they will need a bifocal from that time on. A few rare individuals have mismatched eyes, one near and one far which can allow them to avoid glasses. Not too many of these people out there.