> We have several recent real-world examples of that not working out for the military.

Only when the military is not serious since they are not fighting for their own lands and the civilians are backed by another country. When the military is fighting civilians in its own homeland the civilians stand no chance unless they get massive help from foreign powers.

> Besides, I've always hated this argument, because why fight the military when they can just target the politicians directly.

Even if you do that its still the military that gets to decide the next leader, killing their leader does not lead to democracy. Nazism didn't end with Hitlers death, it ended with the country being taken over. Oppressive Communisms didn't end with Stalins death etc. There are always enough likeminded people that you can't end a horrible reign just by killing the leader.