It looks like the itunes artwork finder in MusicBee caps cover art resolution at 1200x1200 pixels. I was able to find higher resolution artwork with
this website.
It would be great if there was an option to disable the cap.
Another thing I notice is that there are often no matches in the search for cover art. If I search for it manually with a simple google search, I get results. Maybe adding some options to the search (like what tags to search for and where) would help with this.