A Boring Dystopia

It is entirely relevant. By asking what a worker would do if they don't want to contribute to actively managing a company, you are demonstrating a lack of understanding how Capitalist systems function. You're implying Capitalist owners actively contribute and manage the companies they own. Owning stocks and thus a portion of companies doesn't mean you're an active manager, it just entitles you to voting power proportional to your ownership.

If workers owned the Means of Production, then they collectively have voting power, but a worker that does not wish to use said voting power would act just as any other Capitalist that does not wish to exert their power would do: Collect profit and maintain their current power.