Kaydia So, in the E.K.N piece, how would it sound different if there were no slurs indicated?
Then you would play the whole piece non-legato (detached). I find it more difficult to make phrases when playing non-legato, but it can (and should) be done!
Kaydia I feel I am getting the idea of how to phrase a (simple) piece. Well, at least until I came across these 2 pieces. I think I'm getting hung up on what is the purpose of the slur lines if all those notes are going to be connected as a phrase.
It sounds as if you still confuse slurs lines - indicating that you should play legato and not non-legato - with phrases. I have checked the Alfred's book. I see that they are to blame as the ones who gave you this idea.

Also, to add to this confusion, a lot of the pieces in the first Alfred's book don't have slurs, even though most students will play them as if they have slurs.
However, a phrase can be fully non-legato. Or, a slur can stop in the middle of a phrase.
Player1's example is very good.
Do | a-deer | A-fe male deer | Re | A drop-of-|-gold en-sun
Here is another example. You could say that the piece is divided into four phrases that then are repeated. The first phrase does not end when the slur ends, but when the three non-legato notes (chords) end.
Thus, the first phrase is measure 1 and 2. The notes in measure 1 are played legato, the notes in measures 2 non-legato (detached).

PS I see now that they very inconsistently put the slur over the last three similar chords. 🙄