On the other hand, a lot of software is built like bridges. Avionics software (a hefty segment of developers who don't seem to publicly blog much) is built starting with formal requirements documents, and includes formal verification against those requirements, quality audits, signoffs by senior staff and FAA representatives, etc.

Software can be built like bridges. But most software doesn't really need that level of attention, so it isn't built like bridges. In a commercial environment, the benefits of the added overhead would have to justify the expense. I would roughly estimate that avionics-style overhead would quadruple the budget and schedule of your typical web or iOS software project. Is it worth it?

Maybe it'd be worth just being a little more strict, even if not four times as strict. Someone has to make those decisions. But it's certainly possible to take software development more seriously.