I don't think anyone is considering banning cash. More likely, you'll one day find that merchants may refuse to accept cash, or provide change, the same way that many merchants today refuse to accept credit cards. And honestly, that is their right. As someone who's had to collect rent from roommates, I refused to accept cash from them. It's too much of a hassle/liability for me to deal with. I think that a law requiring all merchants to accept cash is government-overreach frankly.
Regarding negative interest rates - this is something that sounds really scary, but actually isn't. We aren't talking about a hard asset like gold - we're talking about fiat currencies. Every time your government expands the money supply and triggers inflation, you're losing money. If you try to prevent governments from setting negative interest rates, they will just pump up the money supply and make you lose money through inflation instead. There's little point in banning negative interest rates, unless you're willing to ban monetary-supply-expansion as well. And unless you're a hardcore Ron Paul libertarian, I bet you've never protested governments promoting moderate inflation.
Regarding anonymous monetary transactions, I agree that there is value in this. This can also be accomplished through cashless transactions. All you need is an aggregated prepaid debit card service. You buy the prepaid debit-card using your regular bank account, and then use that prepaid debit card to conduct anonymous transactions.
The one upside of cash is minimal transaction fees. It always annoys me that Visa takes a 1-2% cut from every single transaction. It effectively makes us all 1-2% poorer in the process. But this is a market-solvable problem if the government took adequate steps to foster competition, and ban anti-competitive tactics. We've already seen many attempts recently, such as Apple Pay, to undercut the credit card companies fees, while still allowing cashless transactions.
Overall, cash is a pain to deal with. If I never had to touch cash again, I'd be a perfectly happy man. I don't think the government should take steps to discourage/ban the use of cash, but if private merchants and individuals decide to abandon cash, the government certainly shouldn't interfere with that decision. The current benefits of using cash can certainly be replicated and had, even in a cashless society.