The traditional norms made us believe that savings are a safe option to store your wealth.
But is it true now?
With inflation, we all know that the prices of the wealth we have kept in our savings account will decrease. What is the use of saving when ultimately we are not even able to enjoy what we have been saving for years?
The smarter option?
Investment! Investment is not gambling if done rightly. Very often we see people not putting too much effort into learning and jumping into FOMO. They dont have enough guidance that will help them to invest better.
You must be reading the wrong books. Traditional wealth management doesn't teach you to store all your wealth in savings. As you said, most of your wealth should be in form of investment: stocks, bond, property, etc.
Savings has its use too. It is not to store wealth but mainly as an emergency fund, a very liquid asset that you can tap into anytime you need a considerable amount of money for an emergency: health emergency, crisis, etc.