You have a pointIts very creative and it is very interesting, but I don't think that the Ninshou connecting everyone can be done in an instant like that, if it was that easy the Sage would have done it rather than run around teaching everyone.
From the sound of it, its more along the lines of a religion that everyone has to accept by their own choice and would require generations to put in place.
Although one explanation might be that Hagoromo traveled around the world to spread peace(as told by Jiraiya)
But this current age, the Shinobi alliance gathered together, there wasn't a need to travel since it was the accumulation of all villages and it was easier to spread Ninshu with them since they all accepted the idea after the war.
I suppose one way I could write it in is that Ninshu was spread across the shinobi. Envoys would be sent to other regions of the globe to do the same thereafter.