A personal account of coming to see correspondences through work in computer science1:
As Heinzi already said in his answer: Even if things becomes worse, the technical Q/A sites of the network (like Stack Overflow) are still far better than most alternatives.
One could do a deep philosophical dive here and think about accumulation and distribution and mechanics of economies. But roughly speaking: In the past 10 years, people could have answered in different forums and could have tried to make different forums and Q/A sites better. But Stack Overflow had (past tense) a goal that was shared by all those who strived to make things better: Create the single, best Q/A site in the world. So it accumulated all the knowledgeable and engaged people who are willing to spend their precious time to achieve this goal.
The model of self-moderation worked astonishingly well in this time. So many people did not only write answers, but also worked in the review queues, trying to minimize the suffering that is caused by the slings and arrows of outrageously bad questions. One could say that Stack Overflow basically "drained" the engaged people from the places where they could have contributed otherwise. But (Heinzi also said that, indirectly) : Even if the quality declines, there will still be enough momentum, particularly on Stack Overflow, to keep the site moving.
So I think the core of the reason of why it will have a limited effect on large network sites like Stack Overflow is:
The effect will not be visible to new users!
Nowadays, when you have a programming question (or error message), you type it into Google, and the "I'm feeling lucky" button could be labeled "I'm confident that the first result is the Stack Overflow Q/A that exactly solves my problem". But one day, people will think that it's normal that you sometimes have to step into the uncharted territory of "Page 2 of the Google search results" to find something that is really helpful. It will be normal that there are many duplicate/cr4p questions that remain on the site, or are even upvoted and answered. We'll be back at the point where there is not a one-stop high-quality Q/A site. But people will not miss what is sometimes referred to as "elitism" when they never really experienced the benefits of it.
1: Mainly referring to Stack Overflow here