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We know that they have to defeat the current Champion to earn the title, but you can clearly choose not to be the seated Champion, as we see the protagonist do time and time again.
They clearly don't have to hang out at the E4, either, even when they are the seated Champion, as Steven still does his research.
This is, of course, mostly conjecture, but I think it needs addressing. What even is the Champion's role in society? Lance helps invade the Team Rocket stronghold, Steven battles at the Space Station takeover, so they obviously are called upon in times of need.