No, FEMA has not been with us forever. There is a nice brief History of FEMA on their website.
Naturally, the creation of FEMA and the changes in mission, focus and organizational structure have come after major disasters.
I can assure you that future changes will be forthcoming--right after the next major calamity or in disaster terms catastrophe.
It would be worth your while to read the history to refresh your memory on how we got to where we are today. I came on the department way back in 1984, just as the first edition of the Federal Response Plan (FRP) was hitting the street. The big debate back then was about "not having" a law enforcement Emergency Support Function.
Today we have the National Response Framework.
One last quick note. In looking up links for this blog post I came across an entry for Lessons Learned Information Sharing (LLIS) which was a popular site "back in the day." I don't know if the incorporation of it into the DHS (Borg) Library in 2015 has helped or not.