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It's a neat idea from a sci-fi perspective, but when you think about the most efficient forms of space propulsion (slingshots around large gravity wells) I'm not sure how we'll manage to do much better.
Either you catch up to someone before they leave the solar system or you're just going to shorten the time needed to reach their terminal velocity.
There's a diminishing return as you approach the speed of light, and FTL travel isn't exactly a trivial hurdle.
You could say that the amount of time it would take for an interstellar trip at non-FTL speeds is also not exactly trivial.
We can sort of try to imagine how technology could develop in tens of thousands of years, but... not really.
We can sort of try to imagine how technology could develop in tens of thousands of years, but… not really.
To some extent, I think we've become blinded by the progress we've made in the last century relative to the progress we made in the millennium before that. For the vast majority of our 10,000 years of human civilization, life was of relatively uniform technological variance. We're in a big uptick of progress in this moment, but eventually (I'd argue very soon) we're going to exhaust the natural limits of our surroundings and the advances of technology will run up against the limits of our material conditions.
Then we very easily could be in a world where the modern day "high tech" nature is the baseline for decades, perhaps even centuries or millennia. Also, very possible we dip into a Dark Age. We've done it before. And its not as though this degree of manufacturing infrastructure is cheap or easy to maintain indefinitely.