I discussed the eighth note rests with my teacher. We've done a fair bit of theory including examining the choices that composers make. Every composer has a musical idea in his head, and then has to use the notation system to bring that across on paper for us to decode and turn back into music. The system is not perfect.
The main idea of the piece is that you have a lyrical melody, with a countermelody along the bass line, both of which should stand out. In the B section the melody switches to the upper notes in the bass clef, and then it switches back. The middle eighth notes are an accompaniment that need to be played a great deal softer, with a light touch. If you let go early knowing that the pedal will continue the note then it's easier to get that touch. (One reason I was not going to do the piece since I'm just starting to get any kind of technique).
In the way it is written you can easily see the steady rhythm that continues on the off beat. If you pedal every beat along with the melody notes, then you will literally hear the middle notes get that shorter note value with the rests. In various performances I've heard, very often beats that have no discordant notes such as beat 2 will only be pedaled once, and there those middle notes sound like quarter notes. I believe we have a choice and don't need to take the rests literally. This part would be interpretation.
The music could have been written with quarter notes or tied eighth notes in part, but it would be awkward looking. I think this way we have greater interpretive freedom. I remember that exploring pedal choices was one of AJS' recommendations and I have to admit I went overboard to the point of ridiculous when I first tried it.