This is what I've been trying to do for over a decade - you can go even further with tee-testing by making a copy of the live traffic you run in a sandbox environment and match responses against. Obviously you can't do some things in the sandbox, email and payments high on that list, but e.g. payment gateway responses can be "borrowed" from production.
Once your new version has no disagreements, it's a really clean swap. I am working towards developing this way and I think, if taken to extremes and carefully, it can remove the review requirement most of the time.