Even deleting your own thread would be useful.
That would be really detrimental. The OP might well not be the main "owner" of a thread. He merely is the one who happened to post about this topic first and your suggestion would allow him to delete other people's content without warning.
As an example then take my EU4 suggestions thread about adding Danish dynamic names. I started it, but I by far is not the only one who has tuned in with valuable data on what is period accurate names for various provinces. Why should I be allowed to delete the well written posts of the other people who posted in that thread merely because I'm the OP?
And especially given that you aren't allowed to open a new thread on the subject if one already exists it becomes really problematic to allow people to delete threads.
And you mentioned OT; the problem becomes even bigger there. Say some big event happens somewhere. One guy will be the first to report about it, but he might well quickly disappear from the thread whereas others, who saw the news at the same time he did, participate way more. Why should he then be allowed to delete their content merely due to being a few minutes quicker to post the thread?
Closing/locking threads on a whim gives similar problem, though not as big as you aren't deleting other people's content.
But it still gives problems. Lets take the case of my Danish dynamic names suggestions thread again. Say it becomes possible to lock threads and I lock it. If somebody wants to continue suggesting even more Danish names he'd then be forced to open a new thread which both is cumbersome for discussion (having to repeatedly refer back to the old thread, where you can't easy quote anymore due to the lock) and it'd also give unavoidable thread spam---especially if it happens several times that the OP closes the thread, somebody else opens a new one on the same topic, later closes, somebody third opens a thread on the same topic, etc. There's absolutely no way of avoiding that thread spam unless you make it a rule that no matter what a new thread can't be started on a topic somebody has already started a thread on, but then you essentially give the OP a monopoly on the topic and permission to decide whether that topic can be discussed on these fora at all! So for instance if some Swede wanted to make sure that no Danish dynamic names were added to EU4 (there were none pre my thread) he could have opened such a suggestions thread and immediately closed it, and I and others would then perpetually be barred from ever discussing the subject...
You can't seriously think that's a good thing.