I imagine for people like my parents, the cost of going to a bank and getting all their suddenly-demonetised banknotes exchanged (which we anyway had very little of) isn't too much. And when some restaurant, say, or a drugstore, is unwilling to accept one of the new 2000-rupee notes, we have credit/debit cards to fall back on. The fact that that people may not have Aadhaar[1] cards or voter ID cards stored safely somewhere, that not everyone has bank accounts which hold >99% (excuse the arbitrary figure) of the money they have, that not everyone has the ability to spend what might possibly be the better part of a day walking to $DEITY knows where the nearest bank is (probably to be turned away because they're out of cash or because the line is a kilometre too long) -- that the very act of going to a bank may not be as trivial or no-brainer-like to everyone as it is to oneself! -- is something we have to work very hard to even imagine. And the cash they have stored is, in many cases, all they have. (Remember what I said about not having a bank account?)
Cash, for us, is what we use for bags of chips and ice-cream and sheets of graph paper and ... bus fare, I guess? Cash, to someone living from day to day, is everything.
edit: yay downvotes, I can tick that off my list