Where I've seen this used before is in unmoderated boards, and they were commonly attacked by spammers and trolls. You could sign in and find there were several hundred posts on a thread since the last time, most of them junk, insults, bad language, etc.
One such was John Jager, aka Mirabile_Auditu, who made a brief appearance here before being shut down by admins.
Where it might be useful is if it were limited to single threads or single posts.
Single posts would mean that instead of X has take note of this post you would show X has ignored this post
The benefit to the person ignored is that they can try to reformulate the post or their argument. Of course you could also modify the "noted button" to be a set of choices:
X agrees with this post
X has noted this post
X has ignored this post
X thinks this post is off-topic
Any one of these would turn off the "has not responded" note on the post, and they also provide feedback to the poster. The link on the thread topic list would just show yes or no to whether a post was responded to (the buttons count as a response).
Another way to implement it in a limited manner would be to have the poster ignored on a thread by thread basis rather than across the board.
As to the comment about it being a way to avoid certain debate points, I don't see this is valid: it can already be done. The benefit would come if the person knows when they are being ignored, as in when you reply to Y you get a message that "Y is ignoring your posts" and this may change the way you write the post, if you still want to.
My experience on those other boards is:
When you ignore someone, you can't see their posts, but can they see yours?
Yes.
If they can see your posts, can they reply to them, it's just that you can't see them.
Yes.
How public is ignore information. Can other people see who you're ignoring?
No. However, I think this information is useful and pertinent.
The benefit is when you are participating in a thread and you have someone with a pet peeve that keeps posting to you regardless of topic or whether or not you want to discuss a point with them, and keeps badgering you to respond to their post/s -- if they make 20 posts to your one, then it can add up to a lot of wasted bandwidth to sort through, ie - troll behavior.
But an "ignore smilies" option might be beneficial. I know one site where (CTD and others) would "debate" by posting a bunch of moving and dancing smilies and no content at all.
™ Version 4.2
