We had a poster (eddie) who spent a lot of time delving into appositives, pretty much on his own. I recall that the term "noun phrase" seemed ambiguous at times.
We name phrases sometimes for the type of word that "fronts" them (heads them), and sometimes for the way the phrase functions as a whole.
So if an infinitive phrase functions as subject of the clause/sentence, you can call it a noun phrase.
To kill a dragon has always been my idea of a real adventure.
My dream, to kill a dragon, has finally been realized.
And of course "gerunds" always function as nouns.
- A.