By default, constraint-based containers will never display scrollbars. The solution is a simple one, and I am simply reposting found knowledge here to hopefully make it easier for others to find. Former Flex engineer Manish Jethani adeptly explains the issue and solution as such:

You can achieve that by setting minHeight and minWidth on the VBox to
0. By the default, the VBox's minHeight is the sum of all of its
children's measured heights (ditto for minWidth), and the VBox won't
resize to smaller than its minHeight, because the Application (which
is a VBox too) gives preference to minHeight over vertical
constraints "top" and "bottom" (and percentage-based heights).

So instead of this:

<mx:VBox top="10" bottom="10" />

use this:

<mx:VBox top="10" bottom="10" minHeight="0" />

Hopefully others find this useful because I was having a heck of a time figuring this out before finding Manish's post. Thanks Manish!