There are lots of blessings where we say Amen at the end, and even lots of places within kaddish where we say Amen, so why at the end of kaddish must we command others to say Amen by saying V'imru Amen (also said in Bentching)?
As an aside, the prompting of "ואמרו" is not found in all early manuscripts of the kaddish, some have "ונאמר".
Dr. de Sola Pool, in his 'The Kaddish' (pg. 42), posits that the idea was to seal closing doxologies as we have elsewhere in the bible where a chapter is ended with the congregation joining in responding "amen" (see ibid. ft. 80). Prior to this prompt the reader of the kaddish petitions for the speedy coming of Messiah and kingship of God, a central theme in Judaism. It would follow that the congregation, after being prompted, responds with the "amen" which serves as an expression of affirmation, acceptance and faith (see ibid. ft. 81).