To be frank, if you're setting up a VPS for a purely static site, you've kinda missed the point of it. Static sites offer so much more potential than just a website that doesnt run server-side code.
If you're going through the trouble to set up and manage your own webserver, you might as well drop some PHP or something into it to get the most out of it.
And publishing a static site locally and deploying via SCP simply will not scale. A big reason why you'd choose a static site is so that you can build and deploy a long, expensive build process on a CI server rather than making the expensive calculations/HTTP calls at runtime. Having CI, you get to simply push to a git repo and know it will be deployed soon, and never have headaches over how long the build or upload is going to take.
You should also take advantage of the fact that a static site can live on a CDN, which will make delivery faster than serving it form a Droplet, and also will never get overwhelmed with huge spikes in traffic.
As others have mentioned, there is a completely different set of hosting providers for static sites: Netlify, Zeit Now, all the major Git hosts provide static hosting, AWS S3+Cloudfront.
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