Pretty certain that you can't go overdrawn on all debit cards. Many banks offer visa debit cards with their basic bank accounts with no overdraft facilities. Also some banks have been known to issue visa debit cards to children, and it would be illegally to let children go overdrawn. So the only feature Nationwide is removing is the free foreign withdrawals.
No doubt one of the drivers is cost, but you might not see it but the debit card argument is actually a very valid argument. Debit card transactions are set to overtake cash transactions this year, and with the introduction of contactless cards I can only see the use of debit cards increasing.
I can see the advantages of free foreign withdrawals, but it seems like it's a thing of the past because as you say there are no other banks or financal companies that offer anything similar for free.
