Recently, an online article mentioned that starting in a few weeks, non HTTPS web pages will be marked as insecure by Chrome.
So I looked at this site over HTTPS and got a warning about unsafe content ahead.
This page had been hosted on Rackspace Cloud files service. I was very pleased with them so far as static website, along with custom domain, was rather straightforward to set up and was working without issues. When used for static hosting, Cloud files are fronted by Akamai CDN. Apparently, this causes issues with SSL certificates so when looking at the secure version of the page, the warning would appear in browsers.
I was unable to find out if Rackspace will in near future support this scenario - HTTPS for static hosting via Cloud files.
So, after some looking around, it turned out that Firebase has a Hosting service which allows hosting of static website with custom domain. Pricewise, the two are almost the same as Firebase is free for hobbyists and Rackspace is essentially free for traffic this blog was getting.
Firebase also has a very modern, developer oriented offering, so I might end up using some other services as well.
Between writing this post and publishing it, Azure has also introduced static website hosting. It still looks a bit complicated to set up, especially the HTTPS story.