It may be the case that people need to carry around cards like they are cash. That is, to keep a card at home or in a bank box that's tied to some other account with emergency funds.
It does say something terrible about our current bank system that nearly everything takes a least day if not a week to process, but keeping around cash won't change that.
Cancelling cards is effortless, and for the CBA, ANZ and Melbourne, your new card will arrive tomorrow, unless it's a weekend.
As to immediate concern for money, you can walk into a branch, and walk out with a card, after verifying identity.
You don't wait weeks. It can take hours.
If you have access to a no-fee credit card, you can also have a back-up at home.
It's probably a good idea to have some cash at home, but you can do the same with cards.