The folk process is alive and well

It's alive in a few, relatively isolated pockets (do kids still sing in playgrounds?), but I wouldn't say it's well.

Rosie - if something appears to be a song that's been preserved through oral transmission, I'd say it's a folk song. As Spleen says, the likelihood of collecting any more folk songs must be pretty slim, but I don't think it's impossible by definition.

Sminky - We compose some kind of statement for future generations explaining why, after centuries of glorious outpouring, no folk songs were created in the 21st century

I already have. (So has Jim Carroll.) The spread of recorded and broadcast entertainment eroded folk song, and the current more-or-less ubiquity of recorded and broadcast entertainment has more or less killed it. It's not a statement about human nature or anything, just historical change.