I doubt that William Eggleston's fame is related to his photographic technique; more best man at the right time.
Eggleston was heavily praised by John Szarkowski the Director of Photography at MoMA and granted a major exhibition in that institution in 1976. Szarkowski was looking to break away from the style of his predecessor Edward Steichen and decided exhibiting color photography would make a dramatic break from the dominance of black and white.
What Szarkowski was looking for was a big collection of really high grade color pictures from one individual. The multi-millionaire William Eggleston had been producing hundreds such of pictures for years for personal creative enjoyment; just what Szarkowski needed.
And it was a huge advantage that the pictures were by an American photographer, of American subject matter, that could be presented both to a high-brow and low-brow American audience.
Szarkowski had been director of photography at MoMA since 1962, so the break with Steichen had been done for quite a while. He had already curated exhibitions from highly original, "non-Steinchen", photographers such as Diane Arbus and Garry Winogrand. He had also, under Steichen, curated in early 1962 at MoMA a retrospective of Ernst Haas' color photography.
Eggleston was far from an unknown quantity at the time of the exhibition, his originality as a photographer had already been recognized, having been granted a Guggenheim fellowship in 1974 and a National Endowment for the Arts fellowship in 1975. He was also already teaching photography at Harvard.
With the Eggleston expo, Szarkowski was simply doing his job as Director of photography. Eggleston was far from the only photographer working with color at the time (the MoMA press release talks about "...a new generation of color photographers"), but he certainly was one that checked two boxes, i.e., not, in Szarkowski's words, "working as if color was a separate problem to be solved in isolation", and, at the same time, still being rooted in the post-Robert Frank aesthetics of "looking at America how it was in the here and now", albeit in a very modern and original manner.