These patterns are built into the key signatures combined with the traditional staff, making them highly visible.
The diatonic notes are visible, but the diatonic pattern of intervals that is consistent across all the different keys is hidden because it is built-in to the staff, out of sight, out of mind.
So to be more explicit with what I mean, the diatonic pattern of intervals that makes up the major scale, and the major keys is:
W W h W W W h
W = whole step, h = half step
If I can't distinguish half steps and whole steps by their appearance on the staff (because they are built into the staff, so that the difference between them is hidden), then I never actually see this fundamental pattern that is common to all keys, and is the source by which the notes in each key are derived.
It's two different ways of approaching and understanding different keys. In the traditional system I learn CDEFGAB as the basic set of notes (with the diatonic pattern already built into them), then each key is learned by altering more and more of those notes with sharp or flat signs. "G Major is the same notes as C Major except for F#, and the tonic is now G." etc. In this approach the musician may never know that the notes of each key follow this same diatonic pattern: WWhWWWh.
In a chromatic staff approach the musician sees and learns this basic pattern of intervals that is common to all keys. Then each key is understood as having that basic pattern (major or minor) but starting from a different tonic note. Instead of building this pattern into the staff, the chromatic staff reveals the interval relationships of diatonic music, the same intervals that one has to play on one's instrument.
Maybe that clarifies what I'm saying? Maybe we will just have to agree to disagree about which method makes the diatonic pattern clearer.
You said:
"When I tried the chromatic staff, everything is invisible and you have to play note for note for note. I can use it if I start circling some of the diatonic things, or put little markers in to tell me things - in other words, duplicate the system that it replaces."
Once you learn how the diatonic pattern looks on the chromatic staff, and perhaps are familiar with the key a piece is in, then you would see the notes as following that diatonic pattern. At first go, it will seem strange and like you're just going note to note.
Also, in those "rough draft" examples no distinction is made between notes in the key and accidentals. This seems like it would be a reasonable thing to show in one way or another (perhaps something like courtesy accidentals just to mark which notes are accidentals). This would surely help, especially for those learning for the first time on such a staff.
(And rather than duplicating the system it replaces, I'd see it as combining the advantages of both...)