No matter what kind of entrepreneur you are, in what industry, business consists of persuading someone to do something. It’s usually persuading customers to buy your product or service, but it might be persuading investors to back you, employees to join you, landlords to give you a break on your rent, readers to subscribe to your blog, etc. Copywriting is simply writing that persuades the reader to take some action.
Slightly single-sided (not all startups sell via websites), but an excellent point, which is not repeated enough.
I'll also add that being a good writer means you can write successful blog posts that can draw traffic and attention to your site. It's a worthwhile investment all around.