I honestly don't understand people who just turn it on and leave it on. To me that's as crazy as always having the flash on regardless of circumstances. HDR is a fantastic tool under the right conditions. If you're using it outside those particular circumstances, you're just making things harder on yourself and won't get as good of pictures overall.
Use the right tool for the job!
In at least the iPhone 5s and 6, it's on Automatic by default and will be used when the OS thinks it will improve the photo. It always stores two copies of the photo (unless you explicitly disable this), so you'll never not have a non-HDR versions. It just means that you'll have two copies of some photos, one of which may be better than the other. I'm not sure why you would turn it off if your phone supports the Automatic option.