In the link he addresses the difference between addressing an acute condition with probiotics versus long-term maintenance of health. Your question seems to land somewhere in the middle. So see what he has to say and please remember, this is far from settled science!
[0] https://humanmicrobiota.weebly.com/prebiotics--probiotics.ht...
The second part is that right now it is somewhat unclear what is actually microbiome related problems. Clearly, associations to all kinds of diseases and conditions have been made, but the casuality and dynamics of the interaction with the immune system and host factors is not well-defined for now. It seems obvious that diseases in which we can intervene with a fecal transplant and improve an outcome are microbiome-related, but there isn't actually that many solid cases for this. C.diff infection is well-established. A recent RCT looks really promising for insulin resistance (i saw the senior author talk about it at a conference and i was certainly convinced), but naggingly insulin resistance wasn't actually the registrered primary outcome of the trial
http://www.stephanguyenet.com/microbiota-and-obesity-is-it-a...
Look at the ingredients on all the products you use. Unless it's Dr. Bronner's soap or something similar, chances it's harmful to both humans and microbes. Just stop using and stop buying that shit!
Sterility is good for the operating table, but not for everyday life.
I don't buy it. I'd attribute the difference more to technologies like vaccines and antibiotics.
If you can disentangle hand washing from the effects of modern sanitation in general, I'm interested to hear more.