Why is full access needed?

No it doesn't mean that "Adobe can read everything on your computer". Nothing has changed from an Adobe perspective...LrC still needs to store its working files (preferences, presets, caches, etc.) in the standard place that it always did, when you want to import images it needs access to the location that you have put them, if Copy is selected it needs access to the location that you tell it to use, and so on. All that has changed is that Apple has tightened it's security, so that some of those locations cannot be accessed without granting the application Full Disk Access. If you are unhappy with this, suggest you speak to Apple.

In the meantime, see this thread for more information and instructions on how to grant that access: https://community.adobe.com/t5/lightroom-classic-discussions/quick-tips-how-to-give-full-disk-access-to-lightroom-classic-on-macos/td-p/12913413