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Should original posters be allowed to delete their threads in a forum?

I don't usually allow that.  There are a few reasons.

If you allow original poster to delete their own threads, you can cause a funky power dynamic where the commenters have to be careful with what they say.  The original poster ends up with as sort of incidental minor admin right that can mess with the conversation.

Also, the subsequent comments may end up more important than the original post.  Often the initial post is just the starter into the real conversation.  The dozens or hundreds of posts after that initial post may be very important to the people who interacted together and have nothing to do with the original post.

If there is a real issue (and there may be), the original poster can contact the admin and the admin can delete the thread for them.

Now... I am speaking about forum threads and depending the specific environment, it may be different.  For example, a blogger should be able to delete his post and comments, but in that case, the power dynamic is understood up front.