The problem with thinking about it on geologic timescales is that humans (and civilizations!) don't exist on geologic timescales.
It's going to be a tough sell to tell people "You need to pay an extra tax for your entire life so we can fund construction of an interstellar ship that your great grandchildren might witness the launch of, but won't arrive at its destination for a thousand years after that."
It's hard to imagine anything that could motivate the human race to do that short of the Vogon constructor fleet announcing that it will arrive within a couple of centuries, ready or not.
I meant https://en.wikipedia.org/wiki/Colonization_of_trans-Neptunia... where they're colonizing those spaces as a place to live -- supposing civilization has already spread through the solar system, we're not talking about needing some kind of super Manhattan project to spread a little farther out. You just need people who feel crowded in the already-full habitats.
Of course this is speculation, but it's one chink in the case for the cost of travel stopping life from spreading. Personally I expect fancier higher-tech faster means in the actual future, like Forward's Star Wisp scheme.
There is precedent: look at the funding and construction of European cathedrals. Often times the people who started on then where dead by the time they were finished
It's going to be a tough sell to tell people "You need to pay an extra tax for your entire life so we can fund construction of an interstellar ship that your great grandchildren might witness the launch of, but won't arrive at its destination for a thousand years after that."
It's hard to imagine anything that could motivate the human race to do that short of the Vogon constructor fleet announcing that it will arrive within a couple of centuries, ready or not.