I think people should be trusted enough to be able to close/lock(un-open) their own thread. It'll stop grave-digging and mild post spamming, people just tend too post on anything they see to get their post count up and it's, irritating. At most times to say the least. It's seems like a good idea I can't see any cons too it. But there might be, if you have any be sure to comment it.
Locking threads is only intended for mods to be able to do it because people would abuse it but I believe people should be able to delete their own threads.