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.