These essays should showcase your very best writing, so if your plan looks anything like Sofie’s, it’s time to start. Supplemental essay prompts for some schools will not be available until August,
Call me cynical, but I think one of the reasons that Harvard does not require a supplemental essay, while every single one of it's peers (YPSM) requires one, is to boost it's applicant numbers. I'm sure thousands of applicants just throw in an application because it doesn't require any extra thought to do so.
Tips for Supplemental Essays - IvyWise
That said, a supplemental essay or other materials are a good idea if you have an extraordinary talent or unusual achievements in a particular field. If you got an A in creative writing, you won’t necessarily want to supplement your application with a stack of short stories. But if one of those short stories got published in a prestigious literary magazine, then it’s well worth sending.