From my experience, the problem with no. 1 is that, in order to build something correct, you have to know what you need to build, and that is a can of worms (actually, a snakes nest) that too many people refuse to address.
The problem with no. 2, on the other side, is that it will eventually get correct, but you cannot predict when it will be reliable. And the same people who refuse to sign requirement documents are the same people who insist on having arbitrary deadlines.
> The problem with no. 2, on the other side, is that it will eventually get correct
Actually, it doesn't necessarily get correct. There are old programs out where the ratio of bugs fixed by a modification / bugs introduced is less than 1. For small systems this never becomes a problem, but huge complex systems it really is a thing.
The only way I know of to prevent it from happening is unit tests with excellent coverage and CI.
The problem with no. 2, on the other side, is that it will eventually get correct, but you cannot predict when it will be reliable. And the same people who refuse to sign requirement documents are the same people who insist on having arbitrary deadlines.