Why is it important that the rocket that just landed take off again so soon?

While that's worded in customer benefit, I think the actual reason is supply-side: hovering is costly, and so landing the stages as cheaply as possible implies doing it quickly.

I've always had the impression that space missions aren't too frequent.

This may be because they are so expensive; if reusable rockets decrease the launch costs significantly enough, there may be many more launches.