If you want formal engineering outcomes, you need formal engineering standards. But in the same way that redoing a home bathroom doesn’t require the same multimillion dollar process as building a bridge, not all software projects can fall under the same umbrella. Any scheme like this has to take into account where certification is actually needed and what the goals and costs are.
And guess what: this already exists. DO-178C for aviation, ISO 26262 for automotive, IEC 62304 for medical, etc. But these standards are specialized to the industry because, no surprise, there is no appropriate one-size-fits-all software development approach. You can’t just say “software must be bug-free” and leave it at that. That’s been shown to be impossible. Even formally verified software can have spec bugs.
There’s already formal standards that CAs must meet, and they get audited too. Maybe those standards aren’t rigorous enough. But even with those standards, what authority is going to punish a CA who breaks them, other than browser/OS vendors? If it damages the host nation, you might see something. But if the host nation is complicit, and used the rogue CA for intel purposes—or if the company has political connections—then I don’t think you’re getting the punishment you want.
It makes sense to have these heavy standards when you’re talking about software whose failure could immediately cost actual lives. I’m hesitant to expand it elsewhere as it could threaten the viability of open source and software freedom in general. Nobody should ever need a license to run a compiler or deploy an application to their own server.