There are lots of reasons why you should take the initiative and do things before anyone asks you to do them. One of those reasons is, of course, that taking the initiative looks good – but that’s far from the only reason.
If you decide to pitch a project rather than waiting for an assignment, you have a lot more control over what you do. When you get assigned something, you have almost none.
When someone asks for something, they spend the entire time between when they asked and when you deliver thinking about the ideal version they could get, and you’re actual version has to compete with that. When you pitch something, you are the ideal version.
When you pitch something, the only outcomes are “they love it; you move forward” or “they don’t love it, but you’re no worse off and even maybe still a little better for showing moxie.” If you have an assignment, completing it well is mostly just treading water, and messing it up can set you way back in terms of social capital and reputation.
Don’t wait for life to give you homework assignments. Decide what you want to do.