Curious what you have found as far as sleeves and shuffle ability. I will use as an example a popular you tube guy, Dale the Casual Gamer (fun guy to watch and this is in no way a criticism of him, Team Covenant, or anyone else who shuffles this way: It is so prevalent it was used as a visual joke in the movie "Tournament", he is just someone I have seen shuffle this way a lot that I suspect a lot of people will be familiar with. I am willing to bet most people reading this shuffle the same way and it is a completely legitimate way to shuffle for this game. Try it in a deal your own poker game and we may have a different answer....) and his manner of shuffling where he holds them horizontal in one hand, pulls a packet loose and mixes them by sliding a few at a time into the main deck in a rapid up and down motion, hitch the main packet to open a new space, rinse and repeat. I only use Dale in case someone is not sure the manner I a talking about and want to look it up.
Anyone who has played in virtually any card game tournament has seen this method dozens, hundreds, maybe thousands of times. Sleeved cards are very difficult to bridge and/or shuffle in the traditional manner. And that is even more true in a casual game like this one where people might use anything from the penny sleeves on to the sleeves specifically designed for the game on up to Dragon Sleeves. Penny Sleeves in particular tend to stick together and get clumps of 4, 5, maybe more cards that move together.
Now, anyone who has done even a cursory study of card magic knows this is a well-loved version to use in shuffling. For the person who knows what they are doing (spoiler alert if you don't want to know anything about how some card effects are accomplished, stop reading this paragraph), this style of shuffle is great because it looks legit and people don't question it but it is incredibly easy to manipulate specific cards to specific location. It is also fantastic, and this is the far more relevant point, for moving packets of cards you need to be together to stay together. Easy way to produce those 4 aces everyone thought were shuffled in to the top to produce. Oh, the magic! That of course is intentional to produce an effect. It will never mix cards as well as a riffle shuffle. Nor will it mix them as well as the time consuming but common in card game circles dealing cards individually to 4,5,6,7 different piles.
I have heard a lot of people talking about getting slapped with Double Advances. I have had it happen myself more than is statistically probable. Fortunately I keep threat so low that is has only cost me a couple times but it is still an issue. I actually started tracking across a couple games, this one and Lord of the Rings LCG to see how much clumping I was getting. I also anecdotally watched when playing someone else's version of Legendary. He uses Penny Sleeves, I use Ultra Pro for LotR and Dragon Shields for Champions. And what I have found is that all of them do not allow riffle shuffle or the hand shuffle method above to give true random distribution in my experience. The same clumps of cards stick together.
One fun way to see how the cards are mixing is to flip them face up as you shuffle for a while. When you see the same 2,3,4,5 cards side by each time and again you visually see this phenomenon.
Now, with Champions the stakes are low. It is a...what is the term tournament players so elegantly criticize Warhammer as...a beer and pretzels game so to speak. By the designers own admission, it is intended for the average player to pick up the unadjusted out of the box hero deck and beat most scenarios most of the time. I can make a pretty strong argument this issue is not really relevant, it is more observation. When you shuffle using this method you are going to find much more frequent instances of multiple expert cards hitting you back to back, more examples of those two "didn't need to see that" villain specific cards in close proximity. You are not getting anywhere near a true random shuffle.
That means you are going to see certain combinations of cards far more often than is reasonable and others far less than make sense. Thor is going to see Hammer Throws back to back and Iron Man will find his armor either all at first or all on the bottom instead of mixed throughout the deck.
Does it matter? That of course is up to individual taste. I actually resleeved all my Champions cards in Dragon Sleeve Matte for better shuffling (lets me riffle shuffle but even there I don't get true distribution as there still tend to be 2-3 card clumps that stick together). I tend to shuffle 15-20 times every time I shuffle trying to get a better randomness knowing the sub-standard shuffleability of sleeved cards when playing solo. When playing in a group I don't bother as it is not real important to that setting which is far more about brothers, nephews, and friends killing pizza, soda, chips and playing a game together for a few hours. But I want to...because I am me. Again, the stakes in this game are low enough that I don't bother.
So what about you? Do you take any extra steps to get a more random distribution or do you just jiggle them together a few times and call it good? Do you care?