Aren’t the dimensions what’s left when rough-sawed 2x4 (or whatever) lumber is planed down for smoothness?
I don't think so, because even rough lumber has actual smaller dimensions. When I want actual dimensions to match design plans, I glue and clamp boards, then cut and plane to exact needed dimensions; what carpenters been doing for years. Even then, boards will shrink and expand with the seasons so that has to be accounted for when building (leaving gaps or allowing boards to move within clamping hardware otherwise boards will warp and break).
I've been in the construction trades for 35 years, and that's the explanation I've always heard.
I was told this when I was a kid - going on 45 years ago — but I don’t believe it. It might have been true once, but that’s a whole lot to “plane down”. OTOH, the actual 2” by 4” two by fours in my 1910 house are rough, not smooth.
I always figured it was the size before kiln drying.