Not your keys, not your bitcoin is still kind of tricky in my opinion.
Personally I've been using Electrum and never kept my Bitcoins in exchange, because once in a while excahnges have been "hacked" and it can be really hard time to get your money back, most likely they are gone forever, but the amount of lost Bitcoins out there already tells how dangerous it can also be to maintain your own keys if you are not careful enough.
I kind of understand if someone doesn't want to maintain own keys and decides to keep them in exchange until it's safer to maintain a wallet. It can also be tricky to keep your seed in safe in some cases.
I would say, when you understand what are the risks in both scenarios and go forward from there you should be fine, not all of us are tech savy in the first place :) You should have a wallet, but no need to rush in the first place.

-I