It certainly has its place, but I've heard of too many people trying to make a switch to it only to get injured. The biggest arguments behind it are that 'it's a more natural way to run' and that 'a lot of Kenyans and Ethiopians do it and they're the best in the world'.
The truth is, they've been running that way pretty much their entire life. You (most likely) have not. Your feet will not be able to handle the beating that their feet can. I have never met a professional runner that identified as a 'barefoot' runner. A lot of runners will work in some sort of 'barefoot' training, but it's minimal and used to build up stabilizing muscles. When a single run can take you over gravel, onto a sidewalk, and through a trail in the forest, it's next to impossible to run barefoot or even with a 'barefoot' running shoe.
You are certainly free to do as you wish, but barefoot running should most likely be used as a tool at best. If you really want to make a complete transition, you would likely need to approach it with the same rigor and dedication someone would use when training for a marathon.
When I run in normal running shoes now, I feel weighed down and I don't do as well. My times have definitely improved, but I think that's mostly because I've been running more because I enjoy it more.
I do not develop blisters nor callouses because the feet are not landing hard and they're not sliding.
A couple of observations then. First, you can't bring your old form and start cold. Be prepared to work up to it by walking and gradually adding running. Second, the new form involves a more bent-knee, hopping, springy aspect. This vid was very helpful for me: https://www.youtube.com/watch?v=Jio7DK15Q1E
It's funny that we learn how to run in diapers and then spend decades learning again.
For better or worse, barefoot forces you to adopt a different gait. Stride length is reduced and landing is shifted more mid/fore-foot instead of heels. Now, can you do this in padded shoes? Sure. You just don't have much choice when barefooting: you will change your stride. If you view heel striking as a bad habit--maybe causing injury--this will prevent that at least.
Personal experience: old guy, unable to run much distance in regular shoes, and after a long conversion period changing technique, I can run a 5k comfortably without injury. Unshod. I'm trying to get up to a 10k. I do wonder if the technique will back-port to regular shoes or if the shod injuries will return.