Not what you're asking for, but you don't need to copy the url, you can just right click on the image and copy it that way. It saves several clicks.
I feel your pain though. I recently re-ripped 2500 CDs, and the rest of my library (about 20k additional tracks) needed better cover art. After doing a few hundred in JRiver, I'm ashamed to say I just paid for dBPoweramp and the cover art extension (PerfectTunes I think it's called?) that pulls hi-res cover art from one of the pay metadata services because I couldn't stomach the thought of doing the rest of that kind of volume in JRiver.
The "hit rate" in JRiver for the kind of music in my library is just too low and getting art from google to JRiver takes a lot of clicks and window swaps when you're talking about thousands of albums. The other software's hit rate was about 90%, and it had an integrated google search for when it didn't have a match. Click on the album once, see their recommended match with the google results right next to it, click the art you want, and it's embedded in the file. You could even amend the search terms in the same window if you thought you could narrow it down. Once I was done, JRiver picked up the embedded art nicely.
Coming out of that massive library renovation, I'm on your page. I feel like the single biggest thing JRiver could do to improve their cover art usability would be including some kind of google image search (or customizable search) integration below the database matches in MC's cover art lookup window. Even just a google search on album artist and album would improve the usability dramatically (cuts out 5 clicks and a bunch of context changes). MC already uses GIS for theater view backgrounds, so it's not entirely new ground.
On the plus side, YADB now has a whole lot of nice new high-res cover art in it courtesy of my "infidelity"