Ovinomancer
No flips for you!
Don't take this wrong, but you haven't thought that through. The odds that you miss by 1 or 2 is just 10% of all rolls. So the near guarantee that the +d6 turns that into success had to be moderated by the chances of it happening to begin with. So, 5% chance of 100% conversion (missed by one) only adds a 5% increase in overall odds. The +d20 works far more reliably than the +d6, with only when you need to roll 17+ on the die changing over. Again, for proficient tasks, you will rarely actually need to roll 17+.If the inspiration is a limited resource, and I know the DC/AC targets, than I'd rather have the d6, since I can choose to deploy it in a situation when I have a 5/6 or 6/6 chance of the bonus shifting the failure to a success.
I'd want the d20 option for when I screw up a save really bad, and the d6 option isn't going to save me.
+d6 favors the non-proficient on hard tasks. In just about every other situation, the +d20 is the better choice (even for thr non-proficent at need rolls less than 17).
The bit about liking the +d6 is mostly confirmation bias for those minority of cases where do miss by 1 or 2. It's ignoring the other cases.