The Colt 1851 .36 Navy (and later 1861 Navy) was their second-most popular cap and ball revolver produced (the first being the 1849 Pocket in .31 calibre). The .36 Navy was used extensively as a combat and defensive arm by frontiersmen, gunfighters both good and bad, lawmen and Civil War soldiers and cavalrymen. Ballistically, it fired an 80 grain round lead ball at 900-1000 fps. It was a preferred sidearm and had a good reputation for accuracy and power, and so was roughly equivalent to modern .380 ACP ball ammunition in energy and penetration.
Which I think leaves the .380 as relevant today in every handgun from pocket-sized to belt-sized, the former being easily concealed, and latter being easily fired. People today are not really any more resilient to gunfire than in the 19th century. For pocket carry, the smaller the better: Ruger LCP, S&W Bodyguard 1.0. For belt carry, a larger size .380 makes for a better grip, steadiness and less recoil: Glock 42, Browning 1911-380, Colt Model M, S&W Shield EZ 380, Walther PP, Beretta 81, SIG P230.
Something for everyone.
The "micro-nines" are noticeably larger and/or more difficult to operate and shoot well. Yes they are smaller than a normal-sized 9mm pistol, but still heavier than a .380, and not any easier to shoot well. I don't like them in a pocket, and I don't like them appendix carried either. If I really needed a powerful handgun I'd choose something bigger that was easier to shoot accurately and rapidly and had better ballistics than a 3" barrel 9mm. I can easily conceal a larger handgun if I really thought I needed it.
For an EDC small handgun, I'd rather have something that was easier to shoot and/or lighter/less conspicuous to carry and/or less problematic and more versatile than a "micro-nine", such as a .380 pistol, or a .38 small-frame revolver.
The "micro-nine" is both an industry effort to sell new guns, and a LE-driven desire to have a single-calibre solution to both on-and off-duty carry. I'm increasingly finding them somewhat irrelevant to the enthusiast who is gun-savvy.