I cheat a bit when I run Leverage and its variants. According to the rules, when the GM spends a PP to create something, it's created at d6. I'm less kind, and when I create things, they're d8s, and for all intents and purposes, I have an infinite budget of d6s that I can use for anything, anytime.
At first blush, that make seem unbalanced and abusive, and I'll concede it's a little mean, but the reality is that it reflects a specific piece of perspective I have about Cortex+, that is to say, what I consider normal to be.
To my mind, in the language of Cortex+, d6 is effectively the die that means "normal". It's the die I pick up to fill gaps when nothing else really applies. If there's a security guard who matters solely because the players eyes have fallen upon him, he's a Security Guard d6. If he matters enough for me to spend some points on, then he should be exceptional (or terrible) and interesting, which merits different dice.
It's also no coincidence that this is the midpoint between the two die values for a distinction. D6 is what D4 is worse than and D8 is better than. Obvious on the face of it, but it underscores why I take D6 as the baseline. If nothing else interesting is going on, just grab a d6.
(Mechanically this also comes in handy when the GM needs to build a small pool. Even if that security guard is a d8, if he's making a roll tangential to any other resource I have in play, it's easier to just add in a d6 to fill out your hand, so to speak)
There's an interesting shift that comes from this, because you stop seeing the world as being built up from zero and more in terms of how it deviates from the norm. It spares you of the obligation to fill in details prematurely. If an NPC is introduced and you don't know anything about him, just use two or three d6s when appropriate until you hit upon the ways in which the character is noteworthy.
This is in some ways a nod back to Over The Edge, where the baseline for any action was 2d6, and you could always fall back to that, but your specific strengths and weaknesses could change that. Having that baseline allowed for much simpler character sheets because it removed the need to note everything, only demanding that which deviated from the norm (and which was, one hoped, therefor interesting). You can see it in other systems too, though it is sometimes more muddled.
This idea bounces around various Cortex+ implementations, but it's precise meaning and role depends on the system. I've noted how it impacts my Leverge play, but it's perhaps even more interesting in Marvel, where the d6 is the placeholder die. Mechanical effects that need a die that's ok use it (like area attacks) dip into it, but for anything interesting, it gets passed by. Ever wondered why there's not a d6 option for specialties? Easy answer: BECAUSE YOU'RE COOLER THAN THAT. I admit, I do dip into d6s for Marvel, but when I do, it's almost always a sign of something mundane - as with Leverage, it's suitable for something that doesn't grab, but which needs mechanical representation.
There's an obvious question here: if d6's are that dull, why bother rolling them? Never make a boring roll, right?
Well, that's the interesting and subtle trick of the d6. It's true, it's not too potent, but every now and again you get boxcars and a surprise. It's important to remember this because normal does not need to mean boring. Rather, it's the baseline by which players can judge themselves. A too-easy success (as many mook rules provide) provide surface awesome but can ultimately feel hollow because anyone can overcome it. D6s have just the right amount of challenge to make your bigger dice feel rewarding and just enough threat to make you wonder if it's _really_ worth trading that d8 for a d4.