Where copy and line editors clean up a manuscript by polishing the prose itself, proofreaders check to make sure those changes came through without introducing more problems. They buff your manuscript to a brilliant sparkle.
Making sure you have the cleanest manuscript possible isn’t just good business sense, it shows you have respect for your reader, too. You don’t want them to get lost in your story because it’s full of errors they have to mentally correct along the way. You want them to get lost in it because it’s that good.
Ultimately, a developmental editor helps you develop as a writer. Sure, they help you write a story that others will want to read, but supporting your improvement as a writer is at the heart of the job. What you learn from a DE for one story should help you as you write future stories.
One of the most important lessons fanfiction writers learn as they write and post their stories, is that having a beta they can rely on for constructive criticism can mean the difference between an ok story and a story that winds up on recc lists long after their favorite show is off the air.