You can get 2 45 inch sticks for the two lower cross pieces and one 48 for the top and end up with one odd peice left over only accasionally. For the height, the choise if to leave this sticking up part, refered to as a rat run to hide cables and electrical cords. Fastening any over head braces needs some spacers applied first but not having things above the wall line actually looks professional and doesn't have anyone wondering what is up here, is that safe? Out of site, out of mind.
It isn't really a mistake, just different. Construction sites have a similar problem and I think I did a whole 1000 SF of cross pieces from reclaimed treated lumber that cost only the time to haul everything and cut it to the proper size. I have two pieces that are my standards for the cross pieces so there is no measuring at all. Just lay and mark. Those very same reference boards never get used for anything but that. Measure twice cut thousands of times.
Another fabulous post from the U.S.Department of Wild Imaginings, now in spectaclar stereo, sponsored by the Adhesives and Sealants Council, suggesting ways to stick things together since the 1800s. Not fabulous in a gay way. Your results may vary. Illinois residents add 8% sales tax. These posts have been made by professional post makers, do not try this type of posting on your own without extensive training, lovely assistants and a trusty clown horn.