I had one. Carried it for about a year. Shot it often, but never got that kind of group. The sights are nearly non-existent, at least for my vision.
One day my brother and I took some auto pistols to the range for some informal testing. I was specifically interested in the difference between the LCP .380 and a +P ammo from a J frame Smith. The .38 did much better (for me) shooting into water-soaked phone books. I could hit better with it, and the heavier Model 36 recoild no more than the light LCP.
However, the weight and bulk of a revolver makes it more difficult to carry. As in all things gun-related, it's a trade off. A LCP in my jeans pocket is more concealable than a .38 in a belt holster, and if one choses to use an inside the pants holster with the J frame, he's going to be wearing it under his shirt against his sweaty skin. That ain't good. On the other side of the question is the power factor. I'm certain that a 125 or 135 grain .38+P is considerably more than any .380 round. One only need view the cartridges side-by-side to see that the .38 is huge in comparison to a .380.
I think everyone who is fond of any particular firearm should take the time to see how it actually works in comparison to something else he might carry. In the end, we find it's a trade off of power vs. size. I like the LCP I had, but I won't buy another. I simply feel I don't have enough power to cancel out potential threats.
I've recently posted on the little NAA .22Magnum I carry, but it is at best a reload for my larger weapon. The LCP is probably the most popular concealed carryr gun ever produced, utterly reliable and accurate enough, but I sometimes think we take ease of carry too far.
Do some expansion and penetration tests yourself before you count on any particular weapon as your only carry gun, is my advice. Compare what you like to carry against a bulkier weapon that's inconvenient. Do a wet phone book or water jugs test. Real results from your own individual weapons can be an eye opener.