Back in 2000, when 3E was shiny and new, there was much discussion of its use of a "core mechanic" of roll a d20+modifiers versus a DC. There's been discussion of it ever since. Maybe there was discussion of it before, but I don't remember it.
Playing a lot of 5E these days, and it's obvious that to the design folks at WotC, they think die rolling is the most important part of a D&D session. Hence the focus on rolling a d20 as a "core mechanic." And yes, I am continuing to use the scare quotes for a reason. It's because WotC completely failed to understand the true core mechanic of not only D&D but of any RPG.
A few weeks ago, discussing things with some 5E people (players, not the design team), I got the distinct impression that many of them were younger and less experienced in RPGs in general than I am. Not that I'm that old. I'll be turning 45 in a few months, and I'm from the third wave of D&D players who started with the Mentzer box sets. I offered the idea that dice are there to be rolled when everything else breaks down, and gave a link to Erick Wujcik's post on The Forge about diceless roleplay. It was one of the key pieces of writing about RPGs that helped me transition out of 3.5/d20 into the OSR (much more so than any of the GNS garbage). I hope I opened a few eyes, but their reaction was hard to gauge. The topic shifted away quickly. Maybe the revelation made them lose some Sanity points! (I keed! I keed!)
Recently, reading Jon Peterson's Playing at the World - more accurately, back to reading it, I'd gotten halfway in and then found myself too busy to continue until this week - he has a section where he talks about the real core mechanic of role playing games.
And that core mechanic is dialogue.
It's one of those things I've intuitively understood from the beginning. And it's where the real fun of role playing is. Sure, there can be die rolls that are high stakes and provide a cathartic reaction when they succeed or fail. Even lower stakes die rolls can have players excited. But the real meat and potatoes is the rhythm of "description, response/question, answer/action, reaction" that comes from dialogue at the table. All of the die rolling is meaningless without it.
So let your game design freak flag fly. Add in subsystems and minigames and weird % Thief skills and weapon vs armor tables (OK, maybe that's a step too far) that don't all rely on a standard mode of resolution. Design games that don't rely only on probabilities with increments of 5%, or a pool of d6's, or whatever.
The dice mechanics are there for when the core mechanic breaks down or isn't enough, as support systems.