Gone are the days when only Tech Leads or project managers were responsible for leading software projects or large features. Nowadays, especially from a perspective of career progression, leading or taking part in the design of large epics as an IC is extremely important.
Why it matters to lead a project
Leading a project is very different from simply collaborating in one as a normal contributor, as it teaches you all kinds of skills:
you see the bigger picture: when leading an effort, it's easier to see the bigger picture of how this effort fits into the organization's roadmap or within the team's work for the quarter. Being knee-deep in technical work makes this harder;
interacting with people: keeping tabs on even one other person besides yourself is a great way to practice leadership skills without actually being a leader. When you manage a project, you end up checking in with your colleagues a bit more frequently and can exercise soft skills more easily;
career progression: as one climbs the career ladder, the higher the steps, the more is expected in terms of being an "integrator": you need to speak with stakeholders in different teams, manage more moving parts, and essentially work at a more impactful level than as a single IC.
Gaining experience
At first, it can be scary to lead anything if you've never done it before, but, the experience and mettle you gain are invaluable in moving you further in your career and increasing your confidence for future similar efforts:
you develop your own style and can learn what works and what doesn't;
your interactions with other people improve the more you do it;
paradoxically, you become a better developer after being on the "other side" - you understand certain trade-offs and decisions better and can apply them to your daily work!
So, next time you have the opportunity, seek to lead an effort and you will learn and grow a lot!