Hi there BertrandRussell. It's a bit of a grey area, this one. If it's a straight TAAT then yes, we usually do just delete as there's generally not a lot to be gained from these threads. If it's more of an 'inspired by' another thread and the OP isn't dissecting the details of one particular thread, then we do sometimes leave them. It really is looked at on a case-by-case basis.
As an example, there was a TAAT tonight that we took down, which you might have seen. There was a really interesting discussion going on, which we didn't want to quash. OTOH, it was a blatant TAAT, plus the original thread had been deleted, so folk weren't even sure that it had been genuine, and the TAAT itself had had a lot of reports that it was turning into a bunfight, then the OP of the original thread turned up to boot. We decided the best thing was to delete it but we did contact the OP separately to let her know we were doing this and to make it clear that she was welcome to start another thread on the same discussion, but it would be best to leave out the references to the original thread.
It is a shame though, we agree, when we have to lose lots of interesting posts to a TAAT, and it's something we'll continue to think about. Perhaps if the only mention is in the OP and the thread is otherwise trouble free, we could look at just editing mentions of the original thread out, with the OP's permission.