The reason why there isn't perfect QA for things like webapps is a cost reason, not a knowledge reason.
Society usually doesn't need a formally proven cat pics sharing app, and most web apps, including facebook, are that level of application. They would rather pay a cheaper price than to have a perfect expensive thing.
You'll also notice that as organizations get bigger, they do invest more in testing, QA and regression detection.
A counter example is in the aerospace industry. Most software has to be d-178b certified, which requires not only testing with complete code coverage, but also complete branch coverage. Every possible outcome in every “if” statement must be tested.
Needless to say, this is expensive. I’ve heard estimates that it costs roughly $1000/line of code.
The point is that there are methods to increase reliability, but there isn’t the financial incentive to do so.
Separate point, I’d argue that small organizations also have quite a bit to gain from a solid testing program.
If there is only a single developer working on a project, that developer can manage much much more code if there are solid tests behind it than if she was just winging it with every commit.
At some point the developer starts to forget the code they write and starts relying on the tests they built long ago.
Society usually doesn't need a formally proven cat pics sharing app, and most web apps, including facebook, are that level of application. They would rather pay a cheaper price than to have a perfect expensive thing.
You'll also notice that as organizations get bigger, they do invest more in testing, QA and regression detection.