Sorry, but I don't agree. That is, a first-person narrator in a novel is an independent persona; that's the case where it does make sense to say, "the narrator." Otherwise, there are two issues:
1) Much lyric poetry is highly personal. When Wordsworth or Mörike writes "I" or "ich," he generally means Wordsworth or Mörike. There are nuances, of course, but very often it's misleading to imply that the poem doesn't voice the poet.
2) So, let's say that you want to distinguish the poetic Petrarch from the biographical Petrarch, and hence you insist on using the periphrasis, despite the fact that the English periphrasis posits that poems are spoken when we all know that they are written and read, far more often silently than aloud. But what's gained from doing so? In a careful study of the differences between the poetic Petrarch and the biographical Petrarch it might sometimes be helpful to use the periphrasis. Not often, though. Even then, normally you can write, "Petrarch says," or "Petrarch writes," and no one will be confused. And then "he writes" (or "says"). Everyone knows what you mean, and you spare me having to read "the speaker," let alone "das lyrische Ich," 40 times in an essay. That's what I meant by unnecessary pedantries. Even where you are right in implying a separation, you aren't telling me anything I don't know by insisting on it over and over; you are just belaboring the prose.