What you're missing: when a question is closed as a duplicate, the link to the duplicate target is automatically put at the top; furthermore, if there are no answers to the current question, logged-out users are automatically redirected to the target.
The goal of closing duplicates promptly is to prevent them from being answered and enable that redirect. As a result, people who search for the question and find a duplicate, actually find the target instead.
It's important here to keep in mind that the site's own search doesn't work very well, and external search doesn't understand the site's voting system. It happens all the time that poorly asked, hard-to-understand versions of a question nevertheless accidentally have better SEO. I know this because of years of experience trying to use external search to find a duplicate target for the N+1th iteration of the same basic question.
It is, in the common case, about personalized answers when people reject duplicates - because objectively the answers on the target answer their question and the OP is generally either refusing to accept this fact, refusing to accept that closing duplicates is part of our policy, or else is struggling to connect the answer to the question because of a failure to do the expected investigative work first (https://meta.stackoverflow.com/questions/261592).