FYI, I've done two things to address this: 1) A muted user cannot PM you. This should have already been the case. 2) Users that haven't yet earned a hubwheel can only send one PM every 10 minutes. Feel free to share suggestions/ideas.
Throttling is what has made me leave a number of other forums, actually. During the "Great Cascade" of 119 days ago, I was undoubtedly excited and posting all over the place. Eventually things settled down and I don't feel as obligated to do so. Dust settling is the most important thing.
So far it hasn't been an issue. When/if it does become an issue, it something worth looking into. Targeting new accounts or accounts with a lot of mutes/ignores can help cut down on the annoyances things like captcha create for non-spammy users.