POSIX compliance is a little high to shoot for when storing binary data inside shell variables, you're not going to get it. This is a BASH script and liable to stay that way. But it can be made a better BASH script.

The question isn't really about compliance, it's about avoiding unintended problems. printf "$randomstring" will mess up whenever $randomstring contains an unintentional % character as those have special meaning to printf. pritnf "%s" "$string" avoids this, but at the cost of not expanding "\x" sequences etc inside $string.