Use DNG to get the most flexibility in image processing. One may select DNG format from either the Camera app, or the third party imaging app.
Selecting the file format that Camera uses makes a big difference in photo quality. The JPG files are very compatible and quick to use, but low quality for many reasons. If one selects the DNG format, and then uses third party software, images can look very good for a camera with such a small sensor and short focal length lens.
I agree with the original poster and others that expect better results, or at least more control over processing.
The real nuisance is that DNG files are not visible to the MacOS Image Capture app unless they are first copied to an album. Some people use ImageCapture to transfer photo files in bulk from their Phone to a file folder on an external drive connected to their desktop or laptop instead of using Photos.
Most 3rd party photo post-processing apps that one might use for their DSLR or Pro camera can work with DNG format. Also third- party Camera apps offer more options, but sadly, they don't launch from the lock screen like the built-in camera does.
Quality is no match for a $300+ camera, but the iPhone does do amazing macro shots as well as great video with good dynamic range and very pleasing stereo sound.
Try not to feel bad about the smeary, melted ice cream with sharpened halos and crudely manipulated images that it makes right out of the box. You can get good photos from the iPhone with a little extra effort.
Warning, Rant Follows:
I too wanted to return my iPhone 13 Pro from the first day I got it. The much vaunted telephoto camera is not worthwhile. There are at least a dozen reasons. In the end, I kept the phone to stay in the Apple universe yet still get security patches.
If Apple offered me a full refund on the phone I bought in December today, I would send it back immediately and then just use my old phone another year. It is really amazing, but the sour combination of expense and kludgey operation smacks a bit too often. It just feels vulnerable to damage, heavy and annoying to use.
It would be nice if DNG files would appear in Image Capture for bulk transfer without Photos. Nice too if all buttons could be reprogrammed so that the side button simulates the old home button, and so that the shutter for the camera is a different button things would be much better for me. Camera is difficult to use with gloves in cold weather. Of course, it would be nice if Apple's camera app leveraged LIDAR features too. All in time perhaps.
Video with decent stereo audio is the forte of the iPhone 13 Pro so far, but even that works best with a popular 3rd party "Pro" app on the phone. But the video works better with a remote control app!
One might wish that Apple had a "tastemaker" again to pull all the pieces together, but those times are only a happy memory. Somehow, still image cameras do not seem to be a priority, especially for young users that expect more from technologies.
Considering the expense of an iPhone 13 Pro with enough extra storage to enable ProRes video, one should expect to buy a little more software and go to a bit more effort to get results that stand out.