A while back I was trying to break down 〜なの, and this is what I decided on (with the help of some of Bart Mathias's posts on mailing lists).
My hypothesis is that the nominalizer 〜の requires everything before it to be in adnominal form (usually meaning, 連体形{れんたいけい} for inflectable words).
In the cases of 形容詞{けいようし} (-i adjectives) and 動詞{どうし} (verbs), the 連体形{れんたいけい} is of course just the 終止形{しゅうしけい}:
- 形容詞{けいようし} (-i adj): 熱{あつ}いの
- 動詞{どうし} (verb): 切{き}るの
In the case of 形容動詞{けいようどうし} (-na adjectives), the 連体形{れんたいけい} is simply adding 〜な, which works out great:
- 形容動詞{けいようどうし} (-na adj): 変{へん}なの
And finally, in the case of 名詞{めいし} (nouns), although they are not inflectable, we can consider both 〜の (possessive) and 〜な as ways to make them "adnominal" (I guess 連体詞{れんたいし} is the right translation into Japanese):
- 名詞{めいし} (noun): 車{くるま}なの
To confirm this theory is actually true, I think the only avenue would be to look in historical texts to see if things like 大{おお}ききの, 死{し}ぬるの, or しずかなるの show up or not. Unfortunately, I am far from being able to do this myself, so I haven't been able to go confirm.
If it does happen to be true, I wonder why the nominalizer 〜の would require things before it to be adnominal. Is の really acting so much like a noun? It seems to be doing so syntactically, but really not so much semantically (from my beginner perspective). The only time it seems to semantically act like a noun is with 形容詞{けいようし} (-i adj) where you can kind of translate it as "thing" into English.
This is my theory, but I'd be happy to hear about a 国文法 explanation if there is one, or an analysis which looks at historical texts.