There is no need for hardware wallet because bitcoin will be stored on a private key no matter what
Well that's one of the dumbest things I've ever read. When you put your Bitcoin in Coinbase you're not holding the funds,
they're holding them for you. And the point of a hardware wallet is to keep your private keys safe - they stop your coins being taken by viruses or hacked accounts.
OP, when you're seeing your Coinbase dashboard you're seeing the coins that you're holding in the Coinbase web wallet (or let's say, the coins that they're holding for you).
When you transfer them out of your Coinbase wallet, they're to an external address. Coinbase doesn't know that it was sent to another wallet that you own, it just knows that you sent it to another address, so yes the number would be gone from your Coinbase account.
I don't see how that would be a problem though, you can just see the balance in your hardware wallet and check the price if that's what you're hoping to do.