I always do it for a reason
You bring up a good point. I agree, they are probably obsolete for certain roles, military for example. But what makes them obsolete for carry is the question then?
For example: When I carry my PT740; If I need to shoot it I draw while at the same time my thumb kicks off the safety. The cocking motion on a single action is pretty much the same.
As to rate of fire, I am more in the aimed shot than volume camp. I think there is definitely something to be said for both the ability to have rapid follow up and a more aimed approach. Even when I carry my P226 and practice with it I shoot at about the same rate as I would when I shoot single.
You mentioned a loading gate vs swing out cylinder. Capacity wise I carry my M85UL alot, and she only has 5 rounds as well. I don't usually even carry and spare ammo. If I was going into combat, my choice in sidearm would be different, probably my P226 or a 1911. But I feel fine with 5 shots for anything I might encounter around town.
Truth be told, I rarely carry spare mags or speed strips for any of my firearms. I usually only do when I am going on a longer road or flying trip.
Age alone doesn't make something obsolete, the city of Rome still uses part of a sewer system build thousands of years ago. DC-3's built in the 1930s are still workhorses and making a living.
In reality "what makes them obsolete for carry" is a question with no answer since we all have our own views. It's just fun to banter it around in my opinion. Even I get tired of debating over politics sometimes.