If I have it right, HEIF is the container, but what makes an image HEIC (the special magic behind the smaller file size while maintaining quality) is the use of HEVC (also known as H.265, the same codec used for similar video improvements at reduced file sizes). It's licensed through the MPEG group, so it should be readily available but there's likely a cost.
If I had to guess, people are having trouble coalescing around a new format partly due to uncertainty and partly due to patents and licensing. Apple's push into HEIF helps, but they're far from the only company who adopted something that had the potential to replace JPEG. Microsoft had JPEG-XR (released in 2009!), which macOS doesn't even natively support. Google has WebP, although they haven't really utilized it in the way that Apple pushed HEIF. HEIF has the advantage of being one of the first to seemingly offer truly significant file size savings while adding other capabilities; in my experience, JPEG-XR is 16-bit but file sizes are larger.
HEIF interestingly isn't the first format to use HEVC encoding. There was a format created in 2014, BPG, that also used HEVC. According to Wikipedia there may have been some patent issues that prevented its widespread adoption.
It is frustrating, though. Like you, I'd like to have 16-bit exported files at reasonable file sizes. For now I've changed my photography workflow to export to 16-bit TIFF and then use a conversion program to convert the TIFFs into HEIC files. I use Permute, a general-purpose file converter, and it works beautifully... but is limited to 8-bit files. Other image conversion software seems to have the same limitation and produces the same results, which leads me to believe that they're calling some macOS-based conversion and the limitation to 8-bit is an Apple-imposed limitation. There is a significant file space savings associated but this workflow takes up a lot more time; I look forward to the day when my imaging software (which supports JPEG-XR and JPEG2000) includes the ability to natively export into HEIF, and hopefully with an option for 16-bit.
