There is absolutely no doubt that Chord Methods are the simplest, fastest and easiest way to learn to play piano. Chord folks play popular tunes utilizing 'fake' books and 'lead' sheets. {'lead' rhymes with freed.}
Chord Method Instructors as a whole can rightfully boast that they have the lowest student failure rates as well as widely available, low-to-no cost printed music. All of which makes the Play-by-Chord category the most successful of Piano Methods. Combining the shortest learning curve with the lowest cost and greatest availability.
However, on average, Piano Chord Methods still produce more failures than successes among their students because all such methods are not even close to created equal.
The worst among the PCM, dragging the whole category down with their high student failure rates, are the 'Chord-yu' folks. Such PCM instructors chord-construction-you into a coma with their talk of 'intervals', scale 'degrees' and so on. All of that just to get you started on your way to finding the 'root spelling' of any given chord. That initial spelling being nothing more than the set of 3 out of the possible 12 piano keys involved in actually playing the chord.
The problem within the mathematics of any such Chord-yu teaching approach is that the Chord Symbols involved become abstract algebra equations in need of solving. Making matters even worse for students is the type of calculation used in solving those Chord Equations. It's an arcane, highly complex form of arithmetic where 2 + 2 = 3.
It's that behind-the-scenes mathematical complexity that gave rise to the Chord-do folks. They do the obvious, cheating their way around the algebra needed to solve the Chord Equations. The Chord-do instructors teach their students to simply look up the root spelling via a chord book, chord calculator or online.
Scott "The Piano Guy' Houston of PBS fame is an example of a Chord-do instructor. His "Play Piano in a Flash" books are both popular and successful. However, as good as Houston is as a Chord-do instructor, he has not yet learned the ways of his unsurpassed competition. The sheet music illiterates best described as the 'Kordy'.
Where the Chord-yu and the Chord-do both struggle their way around the algebra problem with a left-to-right, uphill keyboard approach to learning chords, the Kordy do the opposite. In the process expertly converting the digits on their hands into virtual Chord Calculators.
A mathematically stunning accomplishment that works like having a "Home Row" in typing on a computer keyboard or old manual typewriter.
If the Kordy were into physics instead of piano they'd be starting their students out with Quantum Mechanics. Getting their young totally up to light-speed on the subject in well under an hour.
They do it by seeing things, more like perceiving things, as they truly are. Focusing on only what they need to get the piano playing job done while ignoring the unimportant. As the following set of jpeg diagrams illustrates:
At the top, the first diagram illustrates how Lead Sheet Notation works. Chords are placed above the staff of 5 lines. The Melody placed within the region of the staff of lines. With the song Lyrics placed below the staff of lines. Note the 6 flats in the key signature in the example. That many flats in the key signature generally scares students off from even attempting to play any tune that starts that way.
The next three diagrams are the beginning of Silent Night written in 3 different key signatures, with the middle diagram an example of the totally scary start with the 6 flats.
At the bottom is the Kordy way of looking at that version of the tune. Both the melody and the scary flats of the key signature disappear because they don't matter when you're only planning on playing the chords. Or in this case the chord since there's only one chord in use at the start of the tune, the G Flat major chord. A chord with only 3 piano keys in it.
It's the simplicity of Lead Sheet notation that draws so many students and professionals to playing by chord and using fake books. However it's the Kordy alone who simplify things even more, combining simplicity with the greatest power.