It's pretty simple really. BBC were never going to move the FA Cup conclusion to BBC2 and the news was always going to follow the conclusion of the football.
The news channel comes last in the BBC's list of priorities which is fair enough. BBC want their flagship news show on BBC1 and don't want to annoy people by moving the end of the football to another channel. Whereas in the grand scheme of things delaying the Papers by 45 minutes isn't the end of the world.
But why not just show the game on BBC2 in the first place? That's what many European broadcasters do -- they show all sports events on their second (or third) channels so they don't interfere with the scheduled news programming on their first channel. After all, with digital TV, everyone who has access to BBC1 also has access to BBC2.
Different countries have different TV cultures. Lots of European PSBs only gained a second channel when they launched digital TV (or in some cases earlier than this, but few single PSBs gained a second channel as early as BBC Two arrived) - so they usually have far less history, and far less of a defined 'character' than BBC Two.
In many cases the second channels also don't really have many of their own 'popular' shows - and it's used for repeats of 1st channel shows, extended parliamentary and similar political coverage, repeats of regional news bulletins nationally etc.
BBC One and BBC Two have existed for far longer as a pair, and have very different audiences (and BBC Two has much higher audiences than some PSB second channels)
Big sporting events 'live' on BBC One, smaller sporting events 'live' on BBC Two. People may not see the logic in this, but it's a fact of life. It's nothing to do with universal access.