There  is a slight difference claimed here that switching from Baggi to Elsa and then back again the change in influence is  not not restored.

With regards to influence its not going to make that much difference is it ? Its certainly an impediment when it moves you to a higher league for competitions where the levels required are harder to reach.

The change in influence when you switch shamans is not instantaneous. You need to log out and then back in again to see the change. If this doesn't happen then you need to Ask a question in the Menu.

Yes, the change will make no difference in the run of the game at the time. You will have the correct attributes of the current shaman. But as Anyone says it could be important if someone was trying to switch between leagues for competitions. I can remember struggling for a while to stay below 25M when that was the cutoff for League of Rookies in CvC.

Yes, influence can be bragging but if it's important to the person then it's not unnecessary. I don't aspire to be a 1T player but for some that is the target they have set for themselves and why they spend the big bucks. Also, the highly ranked clans have entry requirements which usually include an influence component.