Your desktop is not really the best place to save individual images, but Lightroom should be able to open them from there. If you can open them from the Pictures folder, then this sounds like you haven't given Lightroom 'full disk access', despite of what you were saying. This is how to do that for Lightroom Classic, but it works the same way for Lightroom:
Reinstalling Lightroom is absolutely useless. This is a MacOS issue, not a Lightroom issue. The folder has the wrong permissions, and perhaps as a result the images now also have the wrong permissions. Do the following. Select the folder and then press Cmd-i. That will bring up the info window for that folder. Look all the way at the bottom. What permissions does the folder show? You should have Read & Write permissions. If you don't have that, then click the padlock, fill in your MacOS login codes and change it. Then click on the small circle with three dots, and choose 'Apply to Enclosed Items'.