We used to think that rates couldn't go negative for exactly the reason you just described.

Turns out that assumption was wrong for a few reasons a) holding onto money is expensive b) in many cases banks have incentive to hold government securities c) sometimes they are outright required to hold government securities d) this is related to (a), but there is risk in holding onto cash where government debt is in many cases perceived as risk-free.

The thought today is that rates can go only slightly negative for short periods of time, which we will continue to believe until some government tries to push the lower bound again.

If you're a giant financial institution, would you want to count, hold, warehouse, secure and move around $100 million in $100 bills? It weighs roughly the same amount as a car.

It's the same reason I keep my money in a bank with no interest even though I sometimes have to pay ATM fees when I need it: the convenience and security offset the costs.

You got some really weird replies. As interest rates go down, people move their money away from treasuries into other assets such as stocks, real estate, etc. Stocks and real estate at least can provide a return, therefore, it's preferred over negative treasuries and cash.

Negative rate treasuries can be preferred over cash because it's owed by the US gov't which has less credit risk than having your cash sitting at some savings & loans credit union in small town in Utah.

Edit: for the other replies: cash in this context does not mean physical paper money.

If you have a large amount of money (e.g., you are a mutual fund), banks will charge you to hold it.