The whole dice thing is fundamental to DND. It's a huge component of the whole tabletop social experience. People have their dice. People share their dice. People watch their dice. People make their dice. People talk about luck in rolling dice. It's hard to imagine playing tabletop with a random number generator.
Yeah, I have my dice that I've been using for ages. My friends call them my loaded dice because they tend to work in my favor. And when others roll them they get crap rolls. lol
All of us have our favorite sets of dice. We also tend to have separate sets based on what we're playing. A set for D&D, a set for Pathfinder, a set for Star Wars, a set for Shadowrun, etc...
Being able to have more dice to choose from would only add to the game. Just don't make them DLC or something stupid like that. Make them tied to your actions in game.