I was thinking exactly the same the other day Kay
Although i'm not sure if MyBB has an option for deleting in selected sections by members (if it doesn't exist yet it ought to as i've seen that certain other forums do have this) i believe there is an option that allows them to delete their thread if there are under X number of posts in it, maybe setting to 3 could work well.
Of course we don't want threads to be deletable on other sections as before, it was extremely annoying to contribute and also see others' valuable contributions disappear just because the thread creator didn't like the turn of the content, but for the market section i think a solution needs to be found.
(I would also like to see the sales threads off the forum statistics page as they have no use there and are masking some more important and useful threads. God knows why certain sales or market threads have to be bumped 100 times or more when the creator could well just delete the former obsolete posts each time.)
Another option could be to bring in another moderator with limited editing rights, we could send them links to the threads we would like to be deleted, someone who has the time to do this.