Lots of RPGs out there use various dice tricks as a part of (or the entirety of) their mechanics. Among these tricks are some of the following: dice pools, gaining additional dice rather than static modifiers, changing results based on odd/even die results, changing die types instead of modifiers, and rerolls.
On the one hand, these kinds of dice tricks are nifty. They manipulate the way the game is played in interesting ways. Also, rolling dice can be fun and satisfying, and fun little tricks are engaging and clever. These tricks might make for easier play, too. For example, looking for the highest roll in a number of dice might be faster than adding a modifier to a single die.
You could, for instance, gain a flat bonus for favorable circumstances to a check, a saving throw, or an attack roll in D&D. Or, you might roll 2d20 and take the highest roll. This dice trick equates to about a +4.5 bonus (so call it +5). Another variant is that you could gain a bonus die to add to your roll. An extra d6 would be like adding a bonus of +3.5 (so call it +4). This latter trick has the benefit of being scalable: A smaller bonus could be a d4 (+2.5), a d8 (+4.5) would be a higher bonus, and so on. Bonuses from different sources could be different dice and you’d just take the highest result (to deal with stacking issues).
On the other hand, such things have never really been a significant part of the game’s history. Flat numerical bonuses have always been at the core of the game. It’s a +5 holy avenger, not a +1d8 holy avenger, after all. Changing the way dice are rolled (or results are obtained) is arguably the biggest, most fundamental change you could make to the game. Should the core mechanic of the game be “roll a d20 and add a number” or “roll 2d20 and take the best result (and probably add a number to that result)”?