How to decrease the height of chooser (file-picker dialog)
The simplest method is to hold  Shift ⇧  &amp; drag by any visible edge of the file-picker dialog. This will resize from all sides simultaneously.

Alternatively, for any open/save file-picker dialog which is not rendered as an attached sheet to the underlying window, you can resize from the top then drag the entire window up, or hold Option whilst resizing which will size from top &amp; bottom simultaneously.

For an attached sheet, the only alternative appears to be to Esc from the file-picker, fullscreen the app, then open the file-picker again.
This will force the dialog to fit the window, allowing you to reach the bottom &amp; resize upwards.  

This size will then be remembered when not in fullscreen.