I'd like to challenge the notion that seems to be prevailing that tunes with simple harmonic structures are in any way bad or unworthy of being a standard. Not a great line of thinking and only contributes to jazz snobbery with no benefit. If a tune is good a tune is good. It shouldn't matter how many chords they managed to fit into it.
I think that's partially true. Since jazzers like to play the changes, many of them like interesting changes. There's no reason why someone couldn't take a great melody with simple, predictable changes and reharmonize it into something interesting, but, I think it's quite a challenge and seems to fail more than it succeeds. To support your case, though, Coltrane used Greensleeves to good advantage, so it can be done.
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