Notes replaced gold and silver coins, if governments make cash obsolete then (some) people will go back to using gold and silver as method of payment, like in the old days.
I don't see why people object to not using cash BTW, personally I have no issue with digital-only currency. Cash is no security against being robbed by the government, we've been lucky here in the UK but in some other countries the government replaced the notes and rendered the old ones valueless (i.e. you cannot even change them at the bank), this sort of thing is very effective in taking away from the public cash money they hosts but can't explain its source.
But, ultimately, if enough people want it, I'm confident that cash will stay with us. Just as the banks tried 20 years ago to make cheques obsolete, but had to make a U turn because people still wanted them. Or, switching off analogue radio... that was announced but then cancelled.