There are 4 reasons we don't:
1. If we release the copyright we have on the text of the song, all that really happens is that the company who owns the copyright to the recordings of the song (also mostly from the 1950's - a 1957 version by Lonnie Donnegan actually reached #1 on the charts at one point) simply gets to keep what they're currently paying us.
2. ASCAP is involved in the legal side of things. I'm not exactly sure how it works, but they're usually pretty vicious about hanging onto the songs they have a right to (and sometimes the songs they don't). Again, it might be that whatever we don't see simply goes to ASCAP.
3. We don't take any kind of steps to enforce it against small performances or individual recordings. So Paul McCartney might have to pay someone who pays someone who eventually pays us, but a high school chorus or a traveling folk singer is not going to run into a problem if they download it from somewhere.
4. My family gives away the money we get to a charitable organization in the region where my grandfather collected the song.
In short, renouncing the copyright only benefits some big corporations at the expense of charity.