highlight all the names/values and right click>copy (this copies all the tags to the windows clipboard). now click tools>remove tags. accept the warning dialog. now right click anywhere in the properties area and select "paste fields" and that will put all your tags back in place.
foobar2000 was never really intended to handle embedding images. I'd be surprised if they added this feature. (And am perfectly happy without it.)
I found some mp3s with embedded album art. I want to delete the embedded cover. Unfortunatelly, right clicking on the cover gives no option such as "Delete cover". Is there a way to delete the cover?
There is API in the SDK for manipulating embedded images (add/remove) as well as reading them, but it's apparently really implemented by the standard input for MP4-based formats only and nobody uses it as far as I know.
MP3Tag can delete embedded albumart.