If Coinbase exchange goes down it's possible that node they are using for their non-custodial coinbase wallet will also go down, so in theory you won't be able to move your coins.
However, you could just use backup seed words and import them in any other compatible wallet and send coins anywhere you want.
I would always give advantage to recommended open source wallets with reproducible codes like Electrum, or hardware wallets like Trezor, Bitbox or Passport.
Just don't keep your coins long term on any centralized exchanges.