Well, I've just picked up a C Sharp book and opened it at random. A G major version of Henry Martin. The 8 bars are harmonised as follows.
/G G/C G/G G/G D/G G7/C G/G C(D7)/G G/

Well, you'd have to try them with the tune, but those chords seem perfectly functional, simple, ideal for the tune.I've just tried them on my guitar. What's not to like? I can think of a great deal wrong with Cecil Sharp's work, and his accompaniments, and have written plenty on the subject myself. But I dont think his G chords are particularly shitty.