My experience has been an issue is raised - usually by management or "the business", but sometimes by engineering. "Our website is too slow!". Now someone has to step up and clarify things. Like: * what does "fast" even mean for our website? It would be great to have an objective metric. * Is there such a thing as "fast enough"? * How much time / effort / money is a given improvement worth? * How do we prioritize this vs. everything else we could be working on?
A project spec comes out of those discussions, but the discussions themselves have significant technical and business inputs.
I don't view taking part in these discussions as "extra" responsibility, I view it as a core part of the job. I've also seen what happens when specs are written without technical input: it makes implementing them a lot less pleasant.