Asking directly for a free copy, unless you have a close friendship or working relationship with the editor, will sound rude. (And if you do have such a close friendship, there's a strong chance you purchased a copy, or you may have even been gifted it.)
What I have done is an extension of a model I use for friends who publish music or books. I never expect to get anything free or at a discount, as supporting their work is important to me, and most of the time each work sold has direct implications on the royalties, etc, that they receive. So instead, I ask them which way of purchasing (directly from them, digital download from a given store, physical copy from a retailer, etc) gets them the most, that way I can also recommend the same method to friends who may want to purchase it.
In academia, I apply the same model, but there's one (not so) small difference: oftentimes, the author/editor has already received all or virtually all that they will get from the book publication, so they don't care if anyone gets a free copy. When I ask, even for books I intend to purchase because they are worthwhile to have in my personal physical collection, I have occasionally been offered a digital copy of the book at no cost.
In reality, this isn't too different than with articles — many of us will happily send out a copy of our articles to someone on request because rarely (never) does anyone make money each time an article is paid for. That and citations.
But, if you go this route, note that you should be fully prepared to actually pay if they offer to personally sell you a copy. It would be at least as rude to reject such an offer after you've effectively said you wanted a copy and were willing to pay $x, and when offered it less than $x, you backed out for cost.