This would enable BW to remain unlocked until the user logs out, rather than having to keep unlocking BW every time the browser is started.
This behaviour can be achieved by installing the “Lightning Reopen” extension, but I see no reason why this could not be supported as BW option without a third party extension.
It has the huge usability benefit of not having to keep unlocking BW all the time, and yet does not requiring storing the encryption key on disk, so it is a much more secure method.
If you don’t want to type your master password and unlock BW each time you open the browser, then you could set to not lock it at all in extension settings - I think this is same level of BW content protection, as you’ve proposed.
But maybe I’ve missed some technical background under your idea…
Yes, you have missed something 
If you set it to not lock at all, then the encryption key is written to disk. This is uncool.
If the browser stays running in the background, then the key is not written to disk, but BW can remain unlocked. This is cool.
Definitely read your reply with a “Bill and Ted” tone. 
We’ll see how the browser extension / desktop app integrations are needed as we bring biometrics to the extensions. Perhaps this could come at some point with that architecture change, but of course further investigation will have to be done.
Thanks!
You might want to take a look at the “Lightning Reopen” extension, because as far as I can see, there’s hardly anything to it. Just set a flag in Chrome or something? Stick the option in BW and it’s all done.