Breaking that promise (e.g. cutting off "dumb" people from the process) means they'll have to find non democratic ways to express themselves. If they're in overwhelming numbers the shortest path is a revolution, and if a gov can just weather a popular uprising, it's a dictatorship.
Looking at 2020 numbers
> children
24% of teens or younger
> foreigners
13%
> criminals
23% of the US population has a criminal record
That's at least 50% of the population. That's a lot for a "weak minority".