I'm thinking about designing some custom dice, and the easiest way to prototype would just be to put stickers/paint on wooden cubes.
Does their fairness (clearly imperfect, especially so with artisanal dice) actually come up in real life, or is die fairness more of a theoretical problem? How can I roll dice so that their "unfairness" is dampened?
How often have you noticed a die being unfair in real life?
I think all it's really possible to say here is that yes, it's a real potential problem. Dice can be unfair, and if they are, you can't really avoid it with rolling technique, and it will skew your game.
I think it's fairly uncommon with commercial games, but I'm not sure how that's relevant to your homemade dice. For what it's worth, my copy of Small World has a wooden die that I eventually found to be slightly unfair (based on test rolls, it has a statistically significant bias), so if it can happen with commercially manufactured wooden dice, I wouldn't be optimistic about homemade ones.
For your actual problem, initial playtesting with custom dice, I would personally just use regular dice with a mapping from numbers to your custom dice faces. If that bothers you too much, or you're to the point where you really need to be prototyping the actual design, I'd put stickers on real dice (preferably blank - it's easier, and they're likely more fair), rather than wooden cubes, so you know they started out as fair as possible, and if the stickers are the same size and placed the same on all the faces, you shouldn't have anything to worry about.
Dice fairness is a real issue, not only in imperfections in the material, which would be more common in wood or any natural material, but also the way the faces are designed, 6 is opposite 1 on a traditional dice, the weight of the 1 side is higher on the traditional die as more is drilled out to make the 6.
There have been many ways attempted to handle this issue in the past, sometimes holes for pips on a die are larger if there are less of them, removing the same material for each size, other times the sides have numerals not pips, allowing for a more equal removal of material, the other largely suggested option is printing or stickers, adding the same amount to each face to show the difference. Some games handle the unfairness of dice by changing the target as time goes on and using a combined score between multiple dice (though multiple dice introduces it's own unfairness as the edge combinations are rarer than the average, there are many more ways to hit a 7 on 2 traditional dice than a 2 or 12), Craps for instance does both of these.
It's definitely not just theoretical - if say in Settlers of Catan one of your dice was unfair, it would skew the probabilities of the number coming up and thus screwing up the strategy.
Fair dice also makes it easier to properly balance the game. I would suggest using website such a http://anydice.com/ to verify your game is properly balanced.
