If at all you had a medical emergency and you did not have an insurance cover, you can use your savings as much as you could have used a medical cover.
Money that you passively save can act like an insurance cover.
It can bail you out when you really need it and do not want to be sunk in debt.
Saving can be good as capital for a small business, depending on how much that you have.
It can help you take a risk and in that sense, you already would be investing.
I do not know why people are advised against saving by some financial advisers.