Is my research statement supposed to lead to papers in top journals?
You do the best you can do with the ideas you have.  Most very good mathematicians can’t come up with a JAMS worthy result every year, and it’s harder when you’re just out of graduate school.  You do need to spend some time on some more ambitious ideas as a postdoc, but “more ambitious” doesn’t mean JAMS-worthy and there’s luck in which ideas pay off and when there’s an unexpected connection that turns up when you’re in the middle of a project.

Yes if you want a job at a top place you might need top publications, but all you can do is do your best with the ideas you have the expertise you developed.  Most of us only get a couple publications at that level in our life.  Aim to be productive and to increase the level of your publications, but thinking about how to get into JAMS or the Annals isn’t helpful.