in your experience are there a lot of good peaceful Muslims who are hoping that the draconian rule of Islam will conquer the world through dawah and big families or is this just a scary fantasy?
In all honesty I think they prefer to not think about it at all. They have this fantasy that once Islam takes over (through dawah and Islamic prophecy) the world will no longer have any issues, it will be this peaceful uptopian society. They don't really want to associate Saudi, Iran, Afghanistan etc with the end result of Islams rule.
They barely think about the end result except in this idealistic fantasy that is vaguely at the back of their mind.
I don't think there are many muslims out there who don't believe the world will one day be completely Islamic, since Islam tells them this will be the case. Some will use force to get there, some will use dawah to get there, but no one I knew was using the breeding way to get there. When they had kids it was just because they had kids, not because it was a step towards any goal.
I doubt they are even totally aware of what sharia law consists of, except maybe the harsh punishments like cutting off the hands of a thief, which sort of made sense back when I was a muslim.
I was subjected to extreme punishments if I did wrong, so the idea of extreme punishment for theft seemed fair, which I know it isn;t, but you'd be surprised how many muslims think that way too.
To them it's not draconian, it is a gift that will creat paradise on earth.