Why boot picker doesn't work?
If you press and hold Option key (on Mac keyboard) or ALT (on Windows keyboard) during boot and there boot picker showing after several seconds, but instead the computer is booting default OS, then you might be using some extra PCIe USB 3.0 card.
Make sure to connect your keyboard and mouse to the built-in rear USB 2.0 hub inside Mac Pro. This should resolve the problem. Also please note wireless Logitech keyboards using Unifying or Bolt adapters, also does not allow to use boot picker.
We recommend either any wired USB keyboard or Apple wireless keyboards.
If you still cannot see boot picker, the resolution is probably too big, so you can't see it. You might need to use underscan feature in your display's OSD.
Some very old DVI displays also might have issues with displaying boot picker, then the only solution is to replace the display with something more modern like Apple Studio Display 27" or a simple Apple Cinema HD Display 20" or 23".