I don't have a lumber dealer near me for hardwoods. A couple of years ago, I did a lot of research into having lumber shipped to me. One of the companies I spoke with pointed out that S2S boards were cheaper shipped to me because the surfacing process removed a considerable weight. This would allow more wood to fit in the maximum size package they could ship without shipping as freight.
Another thing I discovered was that while most of the companies used board feet for their measurement, some of them used the finished size of the wood. If Ocooch Hardwoods, for example, says it is 8 inches wide and 1/2 inch thick, that is what you get.
Each time I purchase wood, I price it out, considering the total cost per foot to get it to my door. So far, the S4S boards from my local big box store have been cheaper. Not by much, but still cheaper. In rough lumber, at least 25% is waste, while there is zero waste in the poplar boards for my local big box stores. The whole board is 100% usable.