Only local image uploads are possible with the customizer

[dpknauss]

Adding images to WordPress through the post editor, theme customizer, or anywhere else requires uploading an image (or selecting a previously uploaded image) in the media library. It's not possible to specify an arbitrary image file by URL or select an image from the media library (for logos, etc.) in the theme customizer, nor is it possible to replace or remove an existing image. This means the media library will accumulate a large number of likely redundant images from typical user behavior where someone adds an image to a post, remove its, modifies it outside of WordPress, and then adds it again. After these actions, both new and old versions of the image will be present in the media library.

[SergeyBiryukov]

It's not possible to specify an arbitrary image file by URL or select an image from the media library (for logos, etc.) in the theme customizer, nor is it possible to replace or remove an existing image.

Appears to be a duplicate of #10950, #20602, and #21483.

[helen]

Duplicate of #21483.