I think your proprioception point is huge. I sometimes randomly get a floppy foot. In anything but structurally sound shoes, I'm wrecked. Would barefoot running have avoided the problem or exacerbated the problem?
No idea, honestly. Normally I'd think a few minutes at a time of barefoot jogging on a soft surface isn't likely to hurt and might help.
You are highly highly aware of your feet when running in shoes with 3mm of total rubber/padding.