My 2 cents:
I'm not going to argue that .380 is a better round than 9mm, or .40 S&W, or .223. I wouldn't use a .380 as my primary home defense weapon. For concealed carry use, I think a couple of things need to be considered: how is the weapon concealed and what is the legitimate range of expected engagement.
If you're going to carry inside the waistband, small of the back, for example, a compact 9mm or .40 is doable. If you want to pocket carry, a .380 is a more reasonable option. Note these are not the only options for concealed carry, just a couple of possibilities. Point is, you need to consider how you will conceal carry and what size weapon you can conceal with that method.
Second, at what range are the threats you expect to have to defend yourself? I would argue that if that range is past a typical self defense scenario, forget concealed carry and tote around an AR. At what range do self defense engagement typically happen? You can find different numbers online, of course, but I would say 7 yards and in is a pretty reasonable expectation. Being accosted approaching your car in a parking lot, for example. That's going to happen at a close range. I still won't argue that .380 is the best round, but within 21 feet I would argue that if you can't or don't want to conceal carry something bigger, a .380 will do the job. As with any other round, shot placement is key.
So, figure out how you will be carrying, test guns you can carry that way, and find out what you can handle and shoot comfortably and put rounds where you want them. Then practice shooting from 2 yards out to 7 yards until you're good. Then practice at these ranges while drawing from your concealed carry method until you're good. Only after this would I worry about practicing at longer ranges.