Purse Engineer Here.
Your Purse <> Coinbase integration scenario is in fact already the case. If you deposit using our Coinbase integration, the transfer happens on Coinbase using their API, and your funds are available immediately in your Purse wallet without confirmations. However all withdraws from our Purse wallet happen on chain. There is no way to transfer funds back to your Coinbase wallet currently without on-chain transactions (I also don’t expect this to happen, it’s a much more complicated integration).
Personally I’m not convinced this is a great solution for everyone; it does potentially create a “walled garden”, and I could imagine services that ONLY offer Coinbase <> Coinbase transfers as a way to deposit funds. I don’t think this is a great solution to the transaction fee issue, but it at least creates a good user experience, especially for novice bitcoin users.