How about the ability to have a second, non-activated card kept at home?
This is an idea that came from a pre-pay user wanting to keep their pre-pay account open after the full launch of currrent accounts. His reason was so that he could access funds should his current account card be stolen or lost. Got me thinking to another thread where someone had a spare pre-pay card that had been sent by mistake and never activated. This guy was offering it to travellers who needed a card quickly during the week where there was a card shortage, as cards are not tied to accounts until they are activated in-app.
So how about Monzo sends a customer a spare debit card which has their account number and name printed on it, but which remains inactive. If the customer loses or has their main card stolen, they freeze their main card, and contact Monzo who can then cancel the main card and bring the secondary card on stream. The customer then activates their card in the usual way as if they had received it in the post.
OK, so it would take some organisation as these cards would have expiry dates and could go out of date without ever being used, but perhaps this is a service that Monzo could charge a nominal sum for, say a fiver? Would be optional, and people could elect to request one if they did not want to have to wait for a new card to be delivered after reporting their main card lost/stolen. Should your secondary card expire unused, you can pay another fiver for a new one.
Revolut provide ‘spare’ cards, for a fee.