There are two reasons why the argument that "the wrong things would change" is the most disheartening of all. First, it says the people are only worth trusting when the outcome is certain. This is fear of democracy. Second, it suggests that protecting particular views and interests is more important than pursuing the broader public interest. This is fear of change.
I'd add that the revision of a state constitution, not to mention the federal constitution, should be an occasion when there are no parties and, ideally, no ideology. Obviously each delegate will have some ideal of how government should work, but the real object of any convention should be the enactment of a practical system of government that would allow any ideological faction to have its way if it can win the support of the electorate, not the enactment of one that would raise ideologically motivated permanent barriers to practical measures desired by the people. The making of a constitution is one of those events that requires everyone to participate in the deliberative process at some stage or other. It's not something anyone should try to prevent because they'd rather not bother or they're afraid they wouldn't get their way. Not everyone gets his way in a democracy, but if you believe in democracy you have to acknowledge that at some level the majority does rule. So let's find out if the people want a convention or not and not worry about how messy or dangerous it might be if they do.