Right, to be able to sight-sing, you need either perfect pitch, or you need to 1) have a sufficient musical theory framework to describe what to sing without perfect pitch 2) need to know how to translate the notes on the page into that musical theory framework. With #2 being the hardest bit.
Having a "simplified musical notation system" might enable many more casual people to be able to sight-sing. But how useful is that, practically speaking? After all, you can just ask your musician friend to play through the melody a few times and then you know it well enough that the full musical notation system can remind you.
In fact, one simple option would be to teach people basic music theory based on C being the root, then write the vocal parts transposed into C and on a C clef. No need for super fancy new notation.
But such a system would have the opposite issue if anyone wanted to play it on a real instrument -- then they'd need to have enough musical theory to be able to transpose whatever they were looking at into the specific key they were supposed to be playing.
Furthermore, if you're looking at music, you're almost certainly going to be playing with an instrument anyway; in which case, you ideally want to practice in the same key the instrument is going to be in. In which case, it's probably better to just teach singers enough piano to be able to plunk out the tune on the piano when practicing privately until they "get" it.
On the whole, it's not clear that any possible improvements to the current system of "Have the people who can't sight-sing listen to the instrument until they get the idea" will be worth the extra costs.