For anyone interested, this is approximately the wait/walk dilemma, specifically the interstellar travel subset: https://en.wikipedia.org/wiki/Wait/walk_dilemma#Interstellar...
I was listening to an old edition of the Fraser Cain weekly question/answer podcast earlier where he described this exact thing. I think he said that someone has run the numbers in the context of human survivable travel to nearby stars and on how long we should wait and the conclusion was that we should wait about 600 years.
Any craft for human transport to a nearby star system that we launch within the next 600 years will probably be overtaken before arrival at the target star system by ships launched after them.
I guess there's a paradox in that we'd only make the progress needed to overtake if we are still launching throughout those 600 years and iteratively improving and getting feedback along the way.
Because the alternative is everyone waiting on one big 600-year government project. Hard to imagine that going well. (And it has to be government, because no private company could raise funds with its potential payback centuries after the investors die. For that matter, I can't see a democratic government selling that to taxpayers for 150 straight election cycles either.)
Yes, my understanding is that the 600 year figure was arrived at assuming that there is iterative progress in propulsion technology throughout the intervening years. But at the end of the day, it is just some number that some dude on YouTube said one time (although Fraser Cain is in fact not just some dude, he's a reliable space journalist (and you can take that from me, some dude on the Internet))