While an interesting idea, I have the same objection to that idea that I have to the idea that life in general is abundant today, which is that we should see the evidence of it. Any truly long-lived society is going to have to engage in some cosmological engineering to survive, and we don't see it.

Furthermore, while any given species might not have survived from so long ago, life itself should never have died out, if intelligent life was common and abundant. The challenges of surviving that era are such that even we can plausibly imagine being able to meet the challenges in a century, or less if we were concentrating.

It's a poetic idea, but the universe does not look like one in which we are some last dying ember living in the carcass of past giants; it looks like one in which there's little-to-no intelligent life in our past light cone.