It does not make sense because software could be written using the same quality standards that CPUs use, which would involve a lot of formal reasoning and proofs.
This work style, however, is not valued at all and is actively suppressed by "flat", non-expert hierarchies that reward people for being popular and sloppy.
It works for web companies because errors have no consequences for them and the web has turned into a gigantic tabloid anyway.
Abstraction layers become simpler, more rigid and more robust as you peel them.
A painter uses rules of thumb all of the time, yet his work is entirely dependent on chemical engineers getting their science and formulas right. Artistic painting is just one of many uses of paint (and probably its most approximate), but both the painter and the industrial product engineer need the same quality assurances regarding their colors.
Hardware needs to be solid to allow all kinds of software the freedom to be built.
I think you also overestimate the formality in CPU design. Yes they do a lot of testing, but it's not lik an airtight mathematical document for the whole chip.
In my experience what trade-off is the correct one depends on your ability to iterate and where your risk comes from. Can you ship infrequently, but you know with high confidence what product/market-fit looks like (extreme example Mars mission)? In that case you want all the planning and verification you can get. Can you ship often, but have little confidence in what your users/customers want and what will grow your business (extreme example social media app)? In this case you probably want to prioritize speed of iteration and rework technical aspects once you know it's what's needed.
I've had a very angry product manager because a feature took almost a second to load. I told him that we could make it load much faster but it would be almost a week of work and he should validate the feature with customers before we invest in that. "Of course we need this feature! It's core to the product!". So we spent a week. It worked realty nicely and scaled pretty well. In the next 12 months the feature changed completely twice because customers didn't find it useful. Then it was removed entirely and then we had to bring it back because the sales team liked it for demos. All that iteration was required to find what the market needed, not fit technical reasons, except for the performance work which was entirely wasted because it all got redone after the first user feedback.
This work style, however, is not valued at all and is actively suppressed by "flat", non-expert hierarchies that reward people for being popular and sloppy.
It works for web companies because errors have no consequences for them and the web has turned into a gigantic tabloid anyway.