This is the reason that there is no public Tahoe-LAFS network also. To run a node on a network like this you need to be brave, much braver than even operating a Tor exit node.
The addition of the long chain activity log may perhaps add some disincentive to upload CP in the first place but getting the economics of that (e.g. ease of getting upload privileges) right sounds like a difficult balance though.
As someone who ran the public facing node with web-interface for the public grid for a while, I can assure you that it is less concerning than running a Tor exit. You will know the IP address of everyone who downloads and uploads from you via the web-interface, and you won't know the data of those who only use your node for storage.
The only complaint I ever received was from Sony after those "Geohot revenge hacks", in which they claimed that a hacked user database from one of their services was copyrighted by them, while at the same time they denied that it actually was the real user database.
We did some searches for the URL of the webinterface and discovered that it indeed was mostly used by "Anonymous" as a Pastebin alternative, at which point it was decided that we did not want to aid in the spread of personal information, which is why it was shut down.[1]
So you are right, there is no public grid because of unwanted files, but not because of Child Porn, but because of some script kiddies.
The addition of the long chain activity log may perhaps add some disincentive to upload CP in the first place but getting the economics of that (e.g. ease of getting upload privileges) right sounds like a difficult balance though.