If we believe that displaying the code of conduct warning is an effective way to reduce unfriendly comments, why not display it whenever someone goes to write a comment? That way everyone can benefit instead of just new contributors.
I recently left a comment on a site that I'm not very active on and almost immediately got a snarky response that reminded me why I don't participate there any more. The comment was removed eventually (I didn't flag it - it didn't really rise to that level for me) but the bad taste lingered. Would someone have been less likely to make that remark if they had been typing it under this?
Be nice and remember to follow our Code of Conduct!
Now, I'm not going to rage quit over one snarky not-exactly-unexpected remark, but I bet dealing with the negativity does make it harder for me to be patient and welcoming. Maybe the impact of preventing me from being exposed to "unfriendly" remarks would also make me less likely to get cranky and make similar comments, and the overall impact might actually be significant. Or maybe it wouldn't do much at all, but the feature is already functional, so what do we have to lose?