The classifieds threads are your threads.
So we can't even clean our own threads without mod assistance anymore? I fully understand the cause for concern in other parts of the forum, but in classifieds, the ability/responsibility to clean a thread should remain with it's creator. Period. Otherwise, all you're doing is giving the mods more power and/or more work to do, of which they need neither.
I think it's mainly because you can just delete your last bump and bump again anytime bypassing the 24hr bump rule.
So it's easier for the mods to remove a useful feature for everybody than it is to address isolated incidents such as your given example? Sorry, but not buying the logic on that one... if that was as major of an issue as you're implying it is, we would have heard about it by now.
Possible solution: Not sure if it's conceivable, but make there be a 24 hour restriction on the ability for the user to delete their own post. Will resolve both the issues regarding cleaning ads, as well as issues involving conflicts in any part of the forum; then the mods can allow for users to delete their own posts ANYWHERE on the forum, not just in the classifieds.
Oh, and some mod/admin feedback would be appreciated, as I mainly want to know if implementing a solution similar to my suggestion is even possible.