It would be a change in the principle behind the Constitution. Rather than a limitation on government, it would be a prohibition against the subjects. Of course, such an amendment would promote objects to be of more importance than the ideas they may stand for; maybe that's what proponents seek.
I believe you are right. Ideas are ephemeral; the protection of ideas requires thought, study, discourse, and a resolute will. Flags are objects; the protection of objects requires a law. Guess which one the legislature finds easier to protect?