Coinbase also does not offer any sort of discounts for on chain transactions as well.
Yes, but I think OP is referring to Coinbase <-> Coinbase off-chain transactions which are free.
But either way, while it sounds so attractive @OP (who doesn't like free transactions?), it's downsides heavily outweighs the upsides. Do you know? Coinbase can lock up your money if they want to? On the other hand, with non-custodial wallets such as Mycelium(though I'm personally more of a BlueWallet[1] guy), no one, I mean literally no one can revoke your access to your funds. That's one of the beauties of Bitcoin!
[1]
https://bluewallet.io/