(May 2022) This is still not functional no matter if you choose High Efficiency or Most Compatible, if you use the built-in camera to take the photo (to upload to a website). It appears all EXIF data is stripped, and I see no option in any settings to avoid this. If you UPLOAD a photo previously taken with the iphone/ipad, the EXIF data is preserved.
There are certain conditions where having EXIF data is not only convenient, but necessary. It seems odd that Apple would intentionally strip EXIF data without any control from the user to choose otherwise. It seems browser agnostic, as far as I can tell.
I see no workarounds. To show this, try my codepen with an iPad or iPhone. Try using the camera first, then try uploading a photo you took with your device and see the difference. https:// codepen.io/zahamm/pen/oNEGbbY