Good point, Murray.

One blatant exception: the one fingering I never* use for G is the one most of us were taught first, with the ring finger on the high E string and the index and middle reaching across to the the low strings. It puts your hand in a completely different position from almost any other chord you'd play before or after a G. (The conventional first-position B7 puts the hand at a similar angle, but those two chords are rarely played one after the other.)

The thumb-on-low-E with index-on-high-E (or on-high-E-and-B) is really just part of the same fingering used for a full third position non-barre-chord G (355433), but I didn't think of it that way when I first resorted to using it.

I should also note that blues players who play in the key of G often anchor their wraparound thumb there on the low E, third fret, while playing all sorts of notes on the top 2 or 3 strings.

*Well, almost never...