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.