I've been allocating some savings to BTC. I keep seeing exchanges fall, and not your keys not your coin. I've been using the Coinbase wallet app. Is that safe?
You already said the answer, so what you're looking for?
If you didn't have your keys while storing your crypto on that wallet which means not your coins. All centralized exchanges aren't ideally good for storing our crypto assets in a long term, all of them are prone to scams that might end up shutting down.
IMO, custodial wallets or centralized exchanges shouldn't be good for storing your coins, they're only good at converting our crypto assets to fiat nothing else. Non-custodial or hardware wallets are much better cold storage if this is your purpose, you have a guarantee that your coins are safe as long as you keep your private key safe.