I have a bluetooth keyboard cover for my ipad - I can type the PIN using the keyboard, no need to touch the screen - it's actually very convenient.

In which case you could still either manually do it (should take no more than a day), or create quite easily a lego-mindstorm or similar device to click on all the combinations "on the screen".

Probably for compatibility with peripheral devices.

Including accessibility for blind users, I assume. Touchscreens are not great input devices if you can't see what's on them or whether you got your finger on the right button.

Accessibility.

iTunes unlock is actually done with a pre shared key during sync.