Yep, there are people that do. Seriously. Here in the 21st Century where carrying any revolver for self defense can get you funny looks there are still people that carry single-action revolvers. Not just a .44 Magnum Blackhawk for defense against bears while hiking, or for hunting where you might expect to see it either. As an EDC. Crazy, huh?
Single action revolvers require you to manually cock the hammer for each shot- but in return you get a short, crisp, light trigger pull which promotes greater accuracy. It also promotes greater likelihood of an unintentional discharge, but that’s nothing that can’t be moderated by training. Modern single-action revolvers can also carry all six chambers loaded with virtually no chance of an accidental discharge if the gun is dropped, so there’s another plus. These guns also generally come in potent calibers like .357 Magnum or .45 Colt. Most of these guns are pretty large, but no more so than a lot of modern ‘combat’ revolvers. Easy enough to carry if you are a large person, and many guns like the Ruger Vaquero or Cimarron Thunderer are available with ‘Bird’s-head’ handles for easier concealment. If you need a smaller gun Cimarron offers their ‘Lightning‘ model with a scaled-down frame and cylinder in calibers from .22LR to .38 Special, even .41 Colt if you are so inclined. With a 3-1/2 inch barrel it’s a pretty handy package.
These guns arguably require extra training, but that’s not a huge issue. So what’s the problem? In a word, reloading. Almost all modern single-action revolvers are slow as hell to reload. You open the loading gate and use the ejector to kick the shells out one at a time, then replace them one at a time. On the range this is no big deal, but if you need to reload in the middle of a fight? Ouch. There is a reason why 19th Century Lawmen and Gunfighters often carried several guns.
OK, yes- there are S&W top-break replicas that auto-eject the shells, and these can be reloaded as quickly as a modern revolver. They are large compared many modern revolvers and are very expensive; I don’t know anyone that carries one as an EDC.
The argument that many make for guns like the J-frame S&W for self defense is that civilian self-defense shootings almost never require more than 2-3 shots, and it’s a valid argument. The odds of a civilian getting into a protracted firefight are almost nil, and a reload is unlikely to be needed. That’s fine, but if you do need to a modern double-action revolver can be reloaded in 4-5 seconds with a bit of practice. In a Colt Style single-action (which is what we’re really talking about here)  a reload will take maybe 30 seconds. That’s a lifetime in a gunfight… if you’re lucky. So why carry a Single Action as an everyday EDC?
Most people that do this carry them because they like them. They find them comfortable and familiar. They are confident in their ability to put shots where they want them. Yeah, they might be better off developing that level of skill and comfort with a modern firearm, but they just don’t care enough to bother. And lets face it, someone points a Peacemaker at you and thumbs back the hammer they are going to get your undivided attention! These things are pretty scary looking from the receiving end.  I’ll tell you this, I’m a lot more likely to be scared of a gray-haired old man with a Ruger Blackhawk than I will be of a gang-banger with a generic 9mm; he’s a hell of a lot more likely to know how to use it!
Then there are the people who just think they are cool, or macho or romantic. The feeling of connection to the ‘wild-west’ gunslinger of old makes them feel good. But like the song says, these guns ‘could get you into trouble but they couldn’t get you out’ unless you are very good indeed.
So is there any good, rational reason someone might use one of these guns for EDC? Surprisingly there is. Some people can’t manage the double-action pull of a modern revolver, and/or have trouble working the slide of a semi-auto. Given that any gun is better than no gun such people might find a single-action revolver, particularly a small frame gun like the Ruger Bearcat or Single-Six, or the Cimarron Lightning might work for them. For these people even an inexpensive single-action .22 like the Heritage Rough Rider is better than being unarmed. Let’s face it, the thing any defensive firearm absolutely must do is go bang when you pull the trigger, and if you can only spend $125 on a defensive gun a Rough Rider is a lot more likely to be reliable than anything else you can get for the money.
I have carried Single-Action revolvers. Mostly when hunting, but occasionally as a defensive carry gun- usually because it was the best I had on hand at the time. Honestly for most EDC I would not feel tragically under-armed with a 3-1/2 inch Cimarron Thunderer or ‘birds-head’ Vaquero in .45 ACP. Would it be my first choice? Probably not. That doesn’t mean I will make fun of you if you choose to. OK, I’m lying,  I will. In a good-natured way at least.