To begin with, unions exist to give workers power in society, where the bulk of the economic and political power is held by those few who control the corporations. When unions make working people more powerful, they are imposing some democracy on a society which otherwise is not very democratic at all. No matter what happens at meetings or conventions, the union will not be democratic unless members control its actions on workplace issues. If members think a bylaws change will make it easier to win grievances, they have a good reason to come to a meeting to vote on it. If an opposition slate has a better idea on how to deal with forced overtime, it may seem worth the effort to campaign for that slate.
Union democracy is about power in the workplace.
Most union members would agree that the United States could use a healthy dose of democracy, especially in the workplace. But that does not automatically mean that democracy is the best method for running a union. If there were a non-democratic way to run unions that gave workers more power in society, against the boss, then members would have to consider it. They say it's a luxury that only gets in the way of unity and swift action. Few leaders will say this in front of the members, of course.