I have a whole selection of handlebars and stems (lots of money spent), I like empirical approach rather than calculations. I don’t think the formula shoulder width = handlebar width is the holy grail, same as with MHR calculation, it doesn’t suit everyone. Anyway, all my bikes came with 44 bars, I’ve been trying different configs stem lengths from 70 to 140, bar widths 36 to 44, that was in the span of over 2 years.
Over that time I understood couple of things…
It all depends on your goals. My goals were to get more solo speed without sacrificing too much climbing ability in races at some expense of comfort. Changing a single thing will impact numerous other things, like saddle tilt, bar height, weight distribution, etc, and while some changes are a clear yay or nay right away, other require to ride for a good while and test in action the setup to understand the real impact of the change. Few things for sure, do not: change many things at once; change things before the event; shorten cables right away; cut the steerer 
But in summary, observations on bar width. Narrow bar is sure more aero, but bike control degrades, especially out of saddle and sprinting efforts will feel lacking control resulting in less power produced. Narrow bars also feel stiffer and more secure when shoulder to shoulder contact is likely to happen - not the bars. Easier to squeeze into tight gaps. Going wider is opposite, so there is a balance there somewhere.
Major changes to bar width and design may require stem change. That may require adjustments to the bar height. Longer gives more stability in straights, but it may upset weight balance and bike may feel twitchy and even cause a so called death wobble, especially when there is too much weight on the front wheel and bar offset approaches or exceeds the trail of the fork. There is also a lot more weight to bear on hands that cause shoulder/neck and hands fatigue. Stem too short will result in more upright and comfortable position. My goal here was to be able to get as aero as possible, but also have straighter back and forearms, good clearance of elbows and knees.
After going to extremities, being 6’2 and wide shoulders I ride 40 bars and 110 stem, giving me a good overall balance on a Large 58 frame.