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This is cool, but couldn't you generate the correction transformation simply from knowing the lens geometry? I assume this is what my phone is doing when I take wide-angle pictures (which don't have any visible distortion)

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Depends on the reason why you are doing this transform. If it's just a visual correction filter, then that will work well enough. If you are trying to track camera movement on a series of images and match a 3D model to the footage, then it's not. You want to analyze the actual images the lens is producing and generate the distortion from that. Every lens is different. Different setups with the same lens may produce different distortions. A warm lens behaves different than a cool lens. Change the focus, and the distortion may change (lens breathing). Some lenses exhibit different distortions at different zoom levels.

Yes. Most professional photo editing and management software has built-in functionality or an add-on for lens distortion correction. However it either requires having the original photo, or at least a non-cropped version with the exif data, or some knowledge of what body and lens and focal length was used.

This utility doesn't require the original non-cropped area nor any other information about the picture that was taken. You could scrape a bunch of pictures from Instagram or Facebook and batch process away.

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