The definition of production seems to contradict what web developers consider an application in production to be. Why is the term in release or published not used instead? I have been in professional web development for ~4 years and we've always used the terminology (development, QA, and production) when referring to the different states of an application. It seems it would be correct to actually refer to development as production and production as release or publish.
Software in itself does not have value. Software can do something that has value. Don't think of software as some kind of widget that pops out of a factory. Instead, the software is the machines in this factory producing the widgets.
Calling it a “production environment” in contrast to a “development” or “testing” environment then appears fairly sensible to me. Of course, this analogy is not helpful for all kinds of software. But it seems very fitting for SaaS offerings.
Or maybe software developers are just prone to redefining perfectly fine words to mean something completely different.