As others have pointed out, Ray did use Hammond, as well as a Continental, a G101, harpsichord, upright piano, etc.
And many of the studio cuts used key bass alone, without bass guitar.
For me, the sound of his combo organs was iconic and Ray (along with maybe Doug Ingle from Iron Butterfly) was the leading proponent of the psychedelic organ sound. It just wouldn't be as special for the music of that era if it was Hammond.
The sustain stops of the Gibson in particular made eerie sounds that could not have been produced on Hammond, and which made songs like "The Unknown Soldier" much more powerful.
But I lived thru that era and was playing combo organs and am probably biased. One thing is for sure - Hammond is a much more versatile and soulful sound. When musical styles changed, combo organs fell out of favor and thus started the age of Hammond.