Is there a way to automatically display one's (own) average rating from all points in time on the diagram for a particular chess variant?
I don't see that option. Have you tried browsing through "chess insights" on your profile page? Gives you loads and loads of statistics.
Yes, indeed, chess insights can be quite helpful. One can probably use "Average Opponent" along with victory rate as a measure (if calculating one by one the average rating manually is not an option...) But an automatic Average Own Rating would be interesting to have I guess...