I think I can answer that question, but it might be in a slightly different way from what you'd expect.
There were a few predecessor organizations to the EIA, but its creation in 1977 was the result of the OPEC oil embargo. The U.S. government and the Congress were getting information, mostly from oil companies, about energy data. They didn't have a source to get its own energy data. Everybody was skeptical of the type of information that was provided by oil companies that had their own interests in providing this data.
The motivation for establishing an agency like EIA was independence, so that it not have any ulterior motives in its collection process, and to be able to collect in a systematic way across all the different sources and uses of information.