There already is a way to fix this... kinda.
Go to "Subscribed threads."
It lists all of the threads you're involved in. If you no longer wish to be involved in that thread, then unsubscribe from it.
The only time I ever use the "My posts" thread is when I want to find a specific post of mine to copy a link to, so I wouldn't ever want to remove posts from it. Otherwise, I use "New Posts" or "New Replies," the first of which checks all new posts in the forum, the second checks new posts only in my subscribed threads.