I feel as if I'm missing something. I've read through the documentation of Jekyll and Hugo, but am still confused as to why one would use them as opposed to something like Pug with Webpack or Parcel to create a static-site.
So, what do static-site generators provide that bundlers don't?
You are comparing apple with oranges here. While all those tools can technically be used to create static websites, they serve different purposes. To quote the header of Jekyll's homepage:
Transform your plain text into static websites and blogs.
Jekyll and Hugo are really designed for plain text and (mostly) blogs. As a user, you write articles in plain text or Markdown, and use those tools to turn them into static HTML sites. Besides generating HTML, the tools have a lot of functionality that is typically needed for blogs, e.g. they create an index of all articles and support categories.
With Jekyll (and probably Hugo, but never used it myself), you can also add pages to your site that are not blog articles. So theoretically, you can ditch the blog and use it to build a static website. But that is probably not why most people use it...
Compare that to Webpack: Webpack is first and foremost a build tool for Javascript. It doesn't care if you are building a static page, a progressive web app or a mobile app. It just bundles your assets based on the configuration you provide. With the right configuration, you can certainly use it for static pages, but Webpack will not offer more functionality than to bundle your files.
Depending on your goal, either of these tools might be better suited for you. Tools like Jekyll and Hugo make it very simple to get started and create a static website or a blog. You can style the HTML, sprinkle JavaScript on it and create your own design. Or you just grab an existing template that somebody else in the community created. Whatever approach you choose, you have something running in minutes.
Tools like Webpack on the other hand give you all the flexibility and a lot of power, but also require that you do everything yourself. It really depends on your use case whether or not it makes sense to build a static site with them.