Inspired by the PbtA mechanics resolution (roll 2d6, 6 or lower = failure; 7 - 9 = success with cost or complication; 10+ = success), which relies of a bell curve distribution of outcomes rather than sheer randomness, is it possible to implement a variant system in 4E without making any other changes? Rather than the three outcomes, this would still be a success or failure (fail forward, in some cases) on the roll against the set DC or defense score: roll 2d10 + modifiers against the DC/defense instead of d20 + modifiers.
From a mathematically persnickety perspective:
2d10 does not have the same mean as 1d20.
3d6, however, does. (An interesting fact that 1E and 2E took much more advantage of than the d20 System editions.)
Obviously, this decreases the random component of such rolls; consequently, perhaps, it may disincentivize or reduce optimization (or, at least, math fix optimization, like expertise and improved defense feats).
It's important to quantify
how exactly the randomness is decreased.
Speaking of 3d6 because of the mean thing...
Imagine a d20 check with a 50% probability of success. A +0 check against DC 11, for absolute simplicity. The probability of success if you switch to 3d6 is still 50%. Half of the results are still above the DC, half below. So the randomness here has changed not at all.
Now give the check a small modifier: +1, still against a DC of 11. The probability of success with a d20 roll becomes 55%. But with 3d6, it's 62.5%. And this gap continues to widen as the modifier increases. By +5, it's 75% for the d20 but over 95% for the 3d6.
So coin tosses are still coin tosses, but modifiers mean more on a bell curve. Or more precisely,
differences in modifiers mean more. Characters who are good at a task find the task much more of a "sure thing", while characters who are bad at the task may find it a near-impossibility. If your goal is to reduce the importance of math fix optimization feats, then, I'm sorry to say that I expect this change to have the opposite effect.