Main drawback to mustache bars appears to be the weird brake position and reach. Most folks I've met locally who tried mustache bars eventually switched back to some form of drop bars, usually wider compact drops.
Best I can tell from conversations, they liked the mustache bars until they participated in large event rides, especially gravel. Then the drawbacks became apparent. It's easier to ride the hoods on conventional drop bars and reach the brakes more quickly. Wide compact drops solved the problem. Still plenty of width for barrel chested folks to breathe freely. Brakes in conventional position.
I use Nitto albatross bars on my old Univega Via Carisma. Very comfortable, brakes within easy reach from the swept back grip position, which is where I'd be in traffic or group rides. On solo rides I can lean forward into the forward arched portion of the bar to get a little more aero and improve hip adductor efficiency. If I had better neck and back flexibility I'd flip the albatross or other swept bars upside down, path racer style.