I think the "completely obscures the relationship between the pitches" is more about the relationship to the tonal than anything else. A note a full step above the tonal sounds the same in any key. When first glancing at a piece of music, the relationship is obscured; to tell something is a perfect fifth from the tonal, you first need to recognize the tonal.
I'm not sure what you mean by "perfect fifth away from the tonal". Do you mean tonic? Perfect fifths are easy to recognize, they're notes which are both on lines or both on spaces, and there is a small gap between them. Yes, you have to remember that one of the fifths is diminished, but only one of them.
Meanwhile, all the thirds are easier to recognize, since they have the same spacing.
I would love to see an alternative notation that is demonstrably easier to read. That is, there's a big difference between "it's hard because music notation is an inherently difficult problem" and "it's hard because the notation we chose sucks".
