> Private. Select this option to make your site private. If you want specific people to be able to view it (and add comments, if you’ve enabled them), you’ll need to invite them to be a viewer.
> I tried using WordPress but it took too many custom plugins and configurations and I still got bombarded by spam signup requests.
One could reduce that amount of spam signup requests that one gets by simplying adding a captca such as recaptcha[0] or hcaptcha[1]
Dropbox is "just" a private s3 bucket with s3cmd on a cronjob -- or a million other technical solutions -- but they're a successful business because they nailed the user experience for average joes.
The point of OP's product is that you don't have to cobble together a bunch of hacks to replicate the desired user experience, it's supported out of the box.
For public signups it is a perfectly valid solution to use captcha!