I could imagine the following use case:
As a habit the user saves the web downloaded picture(s) in that folder "Downloads".
He opens MP3tag to import the picture - and here comes the new way to remember the picture folder: as there is no file in the current audiofile folder MP3tag navigates to the last folder (and the user for the first time to the downloads folder). For all the following imports there is either a file in the current folder or one in the downloads folder ... in this (special?) case the behaviour is quite straight forward.
In the old days (pre 2.51) the Downloads folder was just 2 clicks away as usually there is an extra button for My files in the file selection dialogue.)
I have to be honest: I use the Downloads folder fairly often as I see it as a good collector for any kind of garbage the looks like a good idea keeping when stumbling across. But just as often, as time goes by, the fascination fades and as part of the necessary clean-up the files in that folder go straight to the bin - or the appropriate other folders if they are worth keeping. I see it as rather convenient to have just one place to look at ...
Coming back to the initial problem: as workflows seem to differ so much and looking for covers is such a regular activity, it is probably best to leave the choice to the user ... and create an extra option for the folder selection ...