I realized I've been running a whole bunch of my own smaller projects that way for several years now and I absolutely love it, and now default to it for everything I build
For high stakes systems an alternative I've used that gives much of the benefits while avoiding any risk is Continous Deployment to a staging environment - that way every change is instantly available for manual testing but there's still a deliberate "go live" moment with an extra human in the loop
@simon $dayjob has better test coverage than many projects, but our QA pros still find bugs. Other issues include risk of deadlock deploying schema changes on a large and active database, and customers who dislike being surprised by unannounced changes, even if we do think they're improvements. But automatic deploy to staging (well, scheduled twice a day, plus more on demand when requested) has been a huge win.