What happens in your version of the staff when you start tossing in flats and sharps and double-flats and double-sharps and such?  Is the bottom of the D space now Db and the top of the D space a D natural, then when you use a sharp, it suddenly switches around and the natural is on the bottom?

This is just the first most obvious problem with your variable line system.  

One aspect of staff notation is that serves two masters:  first and foremost it gives the musician the notes to play and the duration to play them.  Secondly, and arguably as important, it reveals the harmonic relationships.  

By means of a contrasting example, I suggest you look at guitar tabulature (tab).  It tells the player where to put his fingers, but reveals NOTHING about the harmonic structure and tonality.  TAB is an example of a positional notation system that if anything obfuscates what's actually going on in the music.

So what happens in your notation when you have a sloppy transcriber?  What about ledger lines?  What happens when the tempo is very fast, and the reader has to differentiate between twelve different locations instead of 9?  In standard notation, we have a key signature that tells us up front which are the "default" sharps and flats.  When reading music that has a key signature, the accidentals "fall out" of the staff and we don't really have to think about them...In fact, because sharps and flats in the staff only indicate places where we're jumping out of key, they are the exception, and fairly rare, and we can then see very clearly and easily that some exceptional transition is coming up.  By contrast, in your notataion ALL of the accidentals are special...which means none are special.

What you're trying to do is interesting, but it can be characterized as trying to "pivot on the wrong axis in the data."  Imagine, if you will, a hardware store nut-and-bolt shelf. How is it organized?  Almost universally, it is organized by function/type as the primary sorting, and by size as the secondary sorting.  You walk in there knowing you need a lag bolt, and when you get to the lag bolts you easily find the 3 inch bolt.  Why isn't it organized the other way around, by size THEN by type?   Because 250 years of usability testing has shown that function.type.size is the natural sort order for people needing fasteners.

So here in this new staff system of yours, you're doing much the same thing.  You're taking a note that was primarily categorized in terms of function, and recategorizing it in terms of size.  That simply doesn't conform to the way people USE the notes.