Coinbase is shit now, a garbage wallet, if you notice then should know that site always down when pump or dump. May be over population or another reason. Blockchain good rather then Coinbase.
I agree with you about Coinbase. They've gone down with no explanation several times, usually when there is market volatility (when you'd most want access to your cryptos). That's unacceptable even for a bank.
There are lots of other alternatives for wallets other than these two, and they're free so try out different wallets and see what you like, that fits your needs.