It is a very big mistake if a person uses all their savings for investment purposes because as you said, savings are not supposed to be used for investments because emergencies can come at any point in life, and when that happens, one would need funds for the emergencies, and in such situations, one wouldn't be able to withdraw their funds from the investments they've made which is why it is important to have savings.
If one can afford this, they should have two funds, one should be their savings and the other should be for investment purposes, so that when they invest their investment funds, they would still have their savings intact and in emergencies, they can use those savings.
Some people have allocated their household saving as emergency fund and scared for using as investment assets, has each allocated as emergency fund or savings assets and some allocated for investment assets. Most of consequence getting when put our money in saving assets and hold it the bank account without increasing the values and must get risk how inflation drop year by year.
I don't think difficult problem with withdrawing investment assets when any emergency needed, saving fund easily for withdrawing but the same with investment fund exactly hold it in cryptocurrency you can sell when do you want without waiting longer time.
Change bad habit with saving money in the bank and move it as investment assets indeed the right opportunity increasing much profitable than have take risk with inflation values when saving in the bank.