Haven is about sharing privately with friends and family. There is no option to make your blog public to the world. You get to create an account for anyone you want to have access. When they connect to your site, they use https encryption between their web browser and your server. That means nobody can intercept and read your posts. Since you create accounts for people, there is no place for spammers or internet bots try creating accounts.
If you want a public blog to build a base of followers, or promote a product, or try to profit from your blog—this isn't the right service for you. I suggest you use Wordpress instead.
> 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!