I'm not even close to suggesting a solution, but to be sure that I understand what you are asking for:
You would like to replace the value in the 'genre' tag with the name of the playlist the file is a part of?
Yes you got it.
I would add that I could still keep the typical genre tags that go with the song, and in addition to add the name of the playlists along with them. So it would looks something like this:
Genre: Rock, Blues Rock, Classic Rock, "PL: Playlist 1", "PL: Playlist 2", "PL: Playlist 3", etc..
Personally I would add the "PL:" prefix to the playlist name in order to keep the playlist grouped together in a list.
So for example... Plex does not allow you to even import any kind of playlist file, which renders it useless to me. If each song had each of it's playlists written to the genre tag, then I could simply import the songs into Plex and arrange by Genre, this would then list all my playlists, along with typical genres... problem solved.
Or in my case, I bought a Fiio R7 Streamer (awesome device), but there is no easy way to import my MB playlists, and even if I did, I would have to reimport them every time I added a new song to one. If they playlists names were written to the Genre tags, all I would have to do is scan/rescan my music collection, then sort/arrange by genre and wha-la! All my playlist would be listed there.
Another benefit is that writing the playlists name to the genre tag is that now that playlist is safe forever... it's saved to the song itself, and travels with the song anywhere it goes. But saved to a playlist file, the file could be corrupted, deleted, incompatible, etc.. and now you lost hours and hours of effort you spent creating that playlist file.
Most applications and hardware allow you to sort by Genre, so it will work instantly with almost anything, with out the need to import any kind of playlist files.
Hopefully that makes since!