For me, software design is more comparable to business system and organization design. It’s just that instead of humans executing the processes you design, it’s machines doing it.
I don’t think business system and organization design is approached like bridge design either, is it?
Also, bridges, houses and surgeons can physically kill people if something goes wrong. Software that can physically kill people, such as that in airplanes or missiles, is actually treated quite differently from most software, I think? I don’t have experience in those industries those so I can’t comment on the specifics of how is it different, but my impression is that things are a lot more rigid. Business organization design also can’t directly kill people.
In general, I think that there is a fundamental tension between looseness and flexibility of operations and innovation. If you are super rigorous and have set in stone best practices, it is going to be harder to find new ways of doing things that work better.
I’m not really bothered if people don’t consider software to be a serious engineering discipline. I’m not sure I do either. If someone wants that kind of thing, I’d recommend they go into a different engineering discipline, rather than trying to make software like that.