As we found out in the privacy review for Autofill Home, Chrome should handle the situations when the screen size is too small (see  https://crbug.com/869343 ).
Instead of one-off fix for the profile chooser we could teach BubbleFrameView to do it because e.g. the site information bubble also suffers from the same problem.

I can imagine the following solution:
- Subclasses of BubbleDialogDelegateView implement a ScrollView (may be for a part of the content) or whatever so that they can be shrunk vertically.
- BubbleDialogDelegateView introduces set_allow_vertical_resize_if_offscreen, false by default.
- BubbleFrameView uses this flag and BubbleFrameView::GetUpdatedWindowBounds resizes the bubble when it doesn't fit the screen.