Sometimes I wonder if a prerequisite to becoming the kind of civilization that
could span a large volume of space is becoming the kind of civilization that has solved the problems that might drive a civilization to need that kind of expansion.
Consider Earth. If we set T=0 at one year ago, and assume that there really is no way around the speed of light, then it follows that by year N, every human alive must be within a sphere of radius N light years.
The average human has a volume of about 0.06 m^3, according to a few sites I found on the net. If you divide the volume of a sphere of radius N light years by 0.06 m^3, you get an upper limit on the number of humans that can be alive in year N.
Given a fixed population growth rate, you can figure out at what year the population hits the upper limit. It is startling faster than you might guess.
At 1% annual growth, we hit it by year 12059, when we'd have a population of 1.04 x 10^62 needing to fit in a volume of 6.22 x 10^60 m^3.
At 0.1% annual growth, we hit it by year 127168, with a population of 1.27 x 10^65 needing to fit in 7.26 x 10^23 m^3.
At 0.01% annual growth, we hit it by 1341545, with 1.45 x 10^68 people needing to fit in 8.56 x 10^66 m^3.
It is clear then, barring faster than light travel (or expansion into other dimensions or parallel universes or something like that), that growth rates for an growing civilization must in the long run go down, and keep going down until growth is very very low if that civilization survives long term.
Keep in mind that my numbers above are the time to hit a ridiculously high limit (packing all space that could be reached at the speed of light starting last year with over 16 humans per m^3). If you use a limit not as ridiculous, such as the still ridiculous limit of all mass within that volume is used to make humans, you'd get a much shorter time to the limit.
I think this might be a candidate for the Great Filter. Lowering growth rates means getting some people not to reproduce, but millions of years of evolution have selected for reproduction. Maybe civilization hit a point where they must slow down growth more than their citizens are willing to do, and that leads to internal conflict that if it does not destroy them at least stops them from further advancing.
The result may be that there may be a lot of civilizations out there, but they get stuck at the first size limit that they hit where (1) they don't have the technology to get past that limit but (2) they have the technology to make war over that limit devastating.
Civilizations that avoid this have figured out how to thrive indefinitely without depending on growth. Such a civilization might not feel the need to expand into a large volume of space. They may be content to stay within their solar system.