The disadvantages are cost, zero interest for your savings and inflation. As you already noticed, with negative interest rates there is a crossover point where it is cheaper to lock up cash than keep it on your savings account.
You might get into trouble with anti money laundering regulation when you take a large sum of physical cash and deposit it into a bank account again at some time in the future.
Additionally, there is the risk of governments seizing the contents of such boxes. The deposit box might also become temporarily unavailable in case the banking system has a meltdown and bank closing. We are talking about catastrophic cases which are rather unlikely and no worse than money in a banking account, but you might still want to consider this to avoid a false sense of security. This also applies to precious metals.
In general, keeping cash - no matter whether physical or in a bank account - is a rather bad investment due to low interest rates. So unless you need this (e.g. as the down payment for a home in the near future) you should consider to invest it properly