That is not the professional way to do things.
Yes there are many years of experience from experienced professionals that have learned to avoid fragile methodologies.
Yet it is closer to a professional solution.
I would not say that but it actually does seem to have happened.
I was a maintenance programmer for many years in a variety of large corporations. We absolutely had a test system to work with. It was very unusual to apply changes directly to production. An example of an unusual situation is what they called Aircraft On Ground (AOG). Emergencies like that.
I don’t know the details of how to have separate test (and temporary release) and production sites using WordPress but large organizations tend to use Git and software such as that. Hosting companies (such as IBM’s Bluemix) used by large corporations support use of Git. See My Git Workflow; it seems to be the type of thing that a business experienced with software systems would want done. Git looks complicated (and I know it is difficult to learn) but it is what professionals do. The original designer of Git was Linus Torvalds, the creator of the Linux kernel.
One term to look for is Configuration Management, as in WordPress configuration management. Oh, and look at that; it does explain that. And WP-CFM seems to be a relevant plugin. Configuration Management Finally Comes to WordPress : Forum One seems to be the developers. WordPress Configuration Management (WP-CFM) | Pantheon Docs seems to be a hosting company that has the plugin installed but I know nothing more about any of those.
The WP-CFM plugin might not help with the conversion from a HTML site. That is where a separate site would help. You could have a site hosted locally within the company or it could be a different domain name or it could just be a subdomain of the production site.