I'll share with you my estimation as to the reason, but I am going to ask you "What benefit did you see in Inspiration?"
Edit: Actually the reason is probably just simply because there is no place put it! lol
Adding it would likely mean that they would have to remove another mastery and I don't think Riot wants to do that. I don't see any one point skill in the Cunning tree that would be worth removing for it and no five point that would be worth it either especially due to the issues of making it require five points.
"Edit" because I don't want to reformat what I wrote before I post. It's mostly for my own benefit but you can read on if you would like.
The reason, I would believe, that Riot did not remake Inspiration is because it didn't seem particularly worth the points you put into it, compared to it's peers, the benefit seemed less usable or worth it. 10 or 20 exp per 10 seconds just isn't enough, in my opinion, when there are minion waves whose experience comes in at 293 per 30. Counterpoint: you shared that exp so it actually works out to like 63 exp per 10 so there is a benefit to increasing exp rate to 131%. Counter-counterpoint: But since you share exp. you would be the same level as the ally for most of the time so the mastery wouldn't even be working for large sections of a lot of the game.
OR the issue could be that if it was included, would they have to buff it to make it worth a mid tier one point mastery spot or to make it worth the five points for a regular one? I think there might not be any middle ground with this one anymore if it was in S6. It seems it would either, if it was a decent strength it would be that each point would be too weak to make it a worth the cost or that it would be strong enough that it would be a mandatory choice.