I think it's hard to get legit, no-shit live cultures to your doorstep and into your mouth. I think the public's opinion of them has outpaced the data supporting their efficacy, however- depending on the condition one is trying to improve.
I would not and I think it seems reasonable to say that nootropic effects of pro biotics are unsubstantiated wrt to good data.I was mainly looking at them for digestion/upset stomach issues, but also for their nootropic effects since the gut has such an integral role of how your cognition and how you feel. The hard part is knowing what strains you need, would you advise sequencing your microbiome with a service like ubiome for that?