I’m a carpenter and framer, and love this sub. Any short answer will do. Love you all!
I am a carpenter too! Depending on what exactly you mean, your answer could be wildly different. If you have ever tried to frame with round material like small-diameter cedar logs you will agree that it is much more difficult to cut accurately or secure tight fits for any kind of structural joint. People have been able to make roughly square boards and timbers by splitting hewing and planing for a very long time and would doubtless have found prepared stock like this preferable when it was available. Where sawmills existed (evidence of a roman sawmill in 3rd century AD in modern-day turkey, fairly common in europe by the late middle ages, earlier in the middle east) truly dimensional stock would have been available, but probably not for even the majority of timber buildings constructed. Advances in sawmilling technology, chiefly thickness planing and edging made boards of approximately standard thickness (2 inch or thereabouts for loadbearing members, 1 inch for sheathing, etc.) increasingly common in the later 19th century. As far as dimensional lumber being "standard," this process began in the united states, in the very late 19th and early 20th century, as university scientists began conducting performance tests on lumber as it came into to use for high performance structures like rail trestles. Scientifically informed municipal code requirements for lumber were implemented after 1915, specifically to allow the safe use of lower grade lumber. By 1940 codes permitted the use of lumber rated at 50% the strength of a completely knot free stud member. Modern dressed 2x stock was first suggested by the US forest products laboratory after world war 1, recommending a thickness of 1 5/8 inches for studes and 13/16 inches for boards. These recommendations were adopted as standard by NLMA, the southern pine assoc. And the north carolina pine assoc. in the early 1920s. These recommendations were developed by a government agency at the request of manufacturers associations, who were struggling to supply the postwar boom in home construction in an organized fashion. Your tl:dr is that lumber became standard in size when it became an industrial product instead of a material which could be custom-processed from the log by a person who, were he not the carpenter, likely knew the carpenter and had a pretty good idea of the intended use of each member he prepared. This transition is compounded by the ever-increasing rarity of large diameter straight-figured trees which can be easily made into quality lumber without a sawmill. More information on the history of lumber standardization here https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.apti.org/clientuploads/pdf/Anthony-Dugan-40-2.pdf&ved=2ahUKEwiS6Zb8y6jhAhUPJt8KHWbiAZgQFjALegQIAhAB&usg=AOvVaw3BfHbemj1wWhCA02NYzt1Z&cshid=1553906336815
To add a little to Gerefa: the real push for standardized dimensional lumber in the US came out of the building boom after WWI. Key to the effort was Secretary of Commerce Herbert Hoover, a mining engineer ( and later President) who had a great interest in generally developing standards. After a lot of meetings throughout the early 1920's, a national standard was reached in 1924. An important part of the push for planing lumber to finish was apparently the Panama Canal opening in 1914: goods shipped by boat were charged according to volume, not by weight, and so there was an advantage to milling lumber to a finished size before shipping.
Sawn lumber continued to be locally sold and used, though. If you look at photographs circa 1925-45 of balloon-frame buildings under construction, a quick indication of whether they're using milled or sawn lumber is whether the crew is all wearing gloves. As you can imagine, no one handling sawn yellow pine or ( worse) Douglas fir would be using their bare hands...or wouldn't do it more than once. Old carpenters like my grandfather tended to call sawn lumber by the actual dimensions, i.e. 2x4, etc, and milled lumber "scantlings", which is the normal term found in 19th c. and early 20th c. builder's books as well.
You can read a detailed history of US lumber dimensional standards here