I agree with the proposal that respondents should not be allowed to change the thread topic.
However, what of existing posts when the topic title is changed? Assume for a moment that, regardless of what is allowed, only the first post's title is altered. My understanding of the current behavior is that existing posts will keep the title they already have, while new posts will take on the title of the OP. According to kieranmillar, quoting the post results in the title being that of the quoted post. I tested this by quoting his post, but it doesn't appear to have done anything to the title - maybe related to the use of quick reply? I have since edited the test out of the post.
I believe the questions at play here are the following:
Should respondents be allowed to alter the title?
Should the title of the first post be alterable?
Should the OP be allowed to alter the title of subsequent posts, and if so, should the title of the first post be updated?
Which should be prioritized for the title of new posts: the most recent post's title, or the original post's current title?
How should changing the title of one post affect the title of other posts?
How should the changing of post titles by moderators work?
My proposal operates on the following guiding principle: the title of the thread as a whole should always match the title of the original post. This suggests that replies should always be given the title of the overall thread by default, and not the title of the most recent post, as automatically updating the original post's topic would be potentially abusable.
Alteration of the original post's title by OP should always be possible - this avoids having to start unnecessary new threads - maybe you want to convert that post you created for your first graphics set to a post featuring all of your graphics sets; or perhaps you've made a major update to a project of yours and wish to update the topic title to reflect that (e.g. Such&Suchlems v1.0 getting updated to Such&Suchlems v1.1).
I have no preference regarding whether OP should be allowed to change the topic title in a reply to the thread, but I think that if such behavior is allowed, the first post's title should be automatically updated. This potentially creates an issue with edits to posts, which could be most easily resolved by only updating the title of the thread if the edited post is OP's most recent posts. That issue could also be avoided by only allowing title edits to the first post, which I would assume to be the simplest behavior.
Titles of existing posts other than the first one should not be altered by changes to the title, so as to keep a record of the title of the thread at the time a post was created. Most of these posts are probably not going to be edited long after posting, so I would leave the titles intact if a change were to be made after the post is created. Alternatively, do replies need a title?
Moderators should always be allowed to edit post titles. The most logical behavior to me would be to allow both isolated changes to a post title, and bulk changes affecting all posts with identical titles (probably ignoring the "Re: " automatically added to the beginning of replies), but the moderators would have a better idea of what their needs are.