I may be old school, but I don't trust these centralized wallets and exchanges because they might be hacked easily. It may happen sometimes to keep a low amount of crypto on a centralized exchange but in general, I keep my funds only on non-custodial wallets.
Your not an old school but I find you a wise guy since we can't really fully trust those centralized wallets and exchanges since they are more prone to any attacks since hackers knows that if they could penetrate in the system they can get a big money from it, I admire you talk about that here since there are so many users who still trust those dangerous options and ignore the past incident of hacking issues.
I always suggest to my friend to always use a non-custodial wallet for good security matters.
Basically to remain cautious and always confident and considerate to make any decision because what makes your funds insecure at least happens to yourself who might easily trust someone or carelessness that ultimately hacks occur, if the problem of an exchange and wallet is centered indeed it is not a recommendation to save large funds but if it is still classified as a small amount of money I am sure it will not be a problem as long as the exchange and wallet are already trusted in the community.