"People in a democratic country wouldn't let their government restrict family size ... would they?"

Yes the would.

Key point by Will Saletan:

What a mess. On one side, we have the Catholic bishops, who are so adamantly opposed to contraception that they're blocking the provision of birth control for voluntary use. On the other side, we have an emerging near-majority of the population that now favors coercive limits on family size. Do the math: The Church claims to represent 80 percent of the population, yet more than 80 percent reject its teachings on contraception, and 44 percent think the government should impose laws in precisely the opposite direction. It looks as though the bishops' anti-contraceptive absolutism is driving their own flock into the arms of a totalitarian remedy.