Most mobster don't wear flashy pinkie rings for the same reason rappers don't wear huge gold chains with larege timepieces affixed to them. (Unless you're a hipster)

That kinda outlandish jewelry accessory was realy only fashionably in the Pre-Gotti era because it was a symptom "disco dandyism"

It's the same reason that mobster don't wear leisure suits anymore.
Simply went out of style.