You're right. Since I'm an introvert myself, I enjoy organizing events and inviting people over, because as the host, I always have a reason to change locations and get some “space” when the socializing becomes too much for me.

This is true as well. If you are otherwise not very social, being the organizer gives you a clear role and clearer expectations and tasks and reasons for people to start talking to you and vice versa. I find this helpful, as unstructured social environments are harder for me.