Swift destabilises the audience by acting as if his proposal is completely serious.
By leading with a serious opening and then switching to something absurd, he is almost testing the audience to see who can be convinced to go along with his argument, and suddenly, the audience has to think about their own attitudes towards the issue as well.
Why would a speaker do this?
Satire is often fuelled by genuine anger at injustices in society, especially those that are large-scale, systemic, and hard to change.
It works by taking the tragic absurdity of a real situation and then expressing it in an even more ridiculously absurd way.
But what's crucial about satire is it takes its own absurdity completely seriously. It "commits to the bit".
In the ad about flooding the Grand Canyon, the "should we flood the Sistine Chapel" headline is not satire; it's sarcasm. The speaker doesn't take it seriously for a moment.
In contrast, Swift spends hundreds of words detailing exactly how his children-eating concept would work, and why it would be a capital idea.