Supers do move a few bees, and they give the bees a place to put the nectar that has been blocking up the brood nest, in effect opening it up a little. At some point, with a prolific queen they WILL over run the hive, and swarming will become the plan.
No one talks about decapping brood frames, or freezing them, (messy, ugly option) but if you do NOT wish to expand, and have no place to put extra brood and bees it is an option that cant be overlooked.
If you do want to expand andmake nuc's/hives then pulling the queen, brood/bees to start another hive or nuc is the way to go. Brood break while they make a queen, some decline while the queen is raised and honey put up rapidly as the amount of brood dwindles and more bees forage.
Beware of waiting too long.. Once they hit swarm mode, they may take the first virgin queen that emerges and swarm with her, so doing this before they start swarm cells is a good idea. Provided you CAN catch them before they start the swarm cells...