When you put your funds on the exchanges, they are in fact not truly yours unless you withdraw them to the exchanges. If any mishap happens, like the exchange is closed or the exchange is hacked, then you will not be able to access the funds and all your money will be lost forever. Furthermore, you cannot go to court and claim your money from exchanges. Therefore, it is not wise to keep the funds on the exchanges.
Not truly yours is a concept foreign to most people and they are using it the wrong way. It is yours, it is basically all yours, as long as the exchange stays honest and actually allows you to withdraw. Same logic as your money in a bank and your money banknotes in your own wallet when we are talking about fiat.
When you have money in the bank, do you really think "this money is not mine"? I doubt many people think that, majority of the world uses banks to store their fiat and majority use credit or debit cards instead of cold cash to spend money around the world. So, long story short your money is still yours and shouldn't be a problem if the exchange allows it to be.