I am experiencing this issue as well. I have a world with around 30 child worlds in it (unlockable universes), and I can not view all of them at a time on the asset manager. Going to the toolbox does not help because it does not display your places for your game. Please fix this Roblox, this is a very frustrating issue!
I believe I have found a solution. This is still a bug, but if you go back to the first screen of the asset manager and then to the page you were at the scroll bar will show up. The issue is that it does not show up when you are adding places or assets from that screen. You have to go back to the asset manager home screen for the scroll bar to show up.
Bump again, this is still an issue, I even made a Feature Request for improving the current state of the Asset Manager, yet nobody has been looking into solving this issue. Many people use the Asset Manager because it streamlines the process of storing content for later use.