I considered when I first decided to learn to read music well. the definition of sight reading as being prima vista kept coming up. Ok, so what is the purpose of that? I would think that it is to get the ability that a pianist would need as an accompanist who is suddenly presented with new material, or someone playing in a group, or maybe a teacher whose student suddenly thrusts something in front of him/her and says "Can you teach me this?" I decided that as a student relearning piano, this was not really the skill that I was after. Which makes me think that the first thing might be to define what the goal is.
I wanted to get the skill of reading music. I needed to become familiar with notes, chords, intervals, and responding to them on the keyboard. From what I know about how we learn, I know that we cannot do more than one thing, or learn more than one thing at a time. As things become familiar, however, several things will already be part of us. So I chose simple music, and I read it over several times. Once I read, concentrating on note names and the corresponding keys. Once I read, concentrating on intervals and naming them as I followed them. Once I read, recognizing the chords. When reading chorales, I might read one voice at a time, then combine two, and eventually all of them, over several days. I might also try recognizing chords.
What happened over time is that I no longer needed to name the notes because they were there for me. I recognized intervals instantly. I came closer to being able to read prima vista at a decent tempo. My thinking is that in learning to read for the first time, we are acquiring various skills that go with that reading, and it is not the same thing as learning to do prima vista sight reading for their usual purposes.