Running barefoot on pavement in the city doesn't work very well. Every time I try it for a significant journey, I can barely walk for a week due to blisters and small glass fragments. Also, people, rightly, stare at me like I'm insane.
I highly recommend barefoot style shoes in general, but you do have to acclimate to them slowly while you build up your foot strength.
After building foot strength in 'barefoot' shoes, I can now run much faster in any kind of shoe.
If you want an almost barefoot like experience, just get very light shoes, like middle-distance spikes, and train on tracks some of the time. Then do your long, easy miles in cushioned road shoes like a normal person.
By the way, my father recalls seeing Abebe Bikila win the 1961 Košice Peace Marathon, barefoot.
I think the notion is to work your way up a lot slower than I did, but I haven't made the same attempt again.