Well, I'm hindered by only having the 2nd and 4th Eds to hand, but I think this is to do with relation-valued, as opposed to composite, domains. A mathematical relation need not be normalised, of course; but the relational data model deals with that subset of relations which are - in the interests of mathematical simplicity.
If Codd relaxed his rules to allow relations of relations (which then can themselves contain relations) this appears to make things more complex (I was saddened when his 12 (13) rules increased in number). But it doesn't make them arbitrary, so I suppose it could be handled...
In theory I'm not too religious about this - as long as you accept the consequences, then relaxing normalisation is fine. In practice, I'm afraid that I think that maximising simplicity results in more resiliant systems - as you say, when you don't normalise eventually you mostly regret it - pace Pick, of course.
30 years ago I felt much the same way about GOTOs: you could use them sensibly and safely but hardly anybody did (or rather, even if they did, this was blown to hell after a little maintenance). I don't think IT's reputation for quality, resiliance and efficient delivery of working systems is such as to justify any of us taking risks, but YMMV.
If one wants to use unnormalised data, one can always use Intersystems Cache - or U2, ADABAS etc. I still suspect it places higher demands on the skill of the programmers involved - although I expect many will disagree with this.