it is that forcing private bein adam l’makom on a large scale is not what the Torah authorizes and it doesn’t do anything to force someone to shake a Lulav if in their mind they are doing nothing.
It’s funny that you should give that example, because the Gemara actually says that we do force someone to do the mitzvah of lulav.
http://www.hebrewbooks.org/shas.aspx?mesechta=31&daf=132b&format=pdf