This is genuinely thought provoking, but (just to play devils advocate here) what about muh cryogenics and muh automation?
Cryogenics, like FTL travel, assumes facts not in evidence: that humans can have their vital processes suspended indefinitely and restarted without damage, despite being in no way evolved for it. Admittedly, it's not as "hard" a limit as the laws of physics, since we know of other organisms that can go into periods of suspended animation for long periods of time such as anthrax spores, but they're far smaller and simpler than we are.
Furthermore, any such technology would need
extensive testing once invented, since if we don't know that our generation ships' technology will keep us alive for generations, all such ships might be simply extraordinarily complex and expensive premature tombs for our species' best and brightest, launched into the darkness of interstellar space like the world's most metal version of Viking funerals. If you want to make sure your cryogenics systems work for generations, you need to test them for that long; Bob is definitely not going to live long enough to see the conclusion of any such test even if one started tomorrow. Just as well; sending frozen Bob into the unknown universe is the first contact version of dialing a random number, then holding the phone up to your butt and farting.
Automation isn't in a much better state. Again, we would need to be sure that our systems would work for decades without maintenance (if the crew is cryogenically suspended), or we are allowing our crews' technical skills to decline without practice (if we use automation to make up for slackness on the societal engineering side). Also, you can't have a repairer machine to repair the repairer machine that repairs the repairer machine (etc., forever); you need a general-purpose system that can repair anything, including itself. And there's the problem of what the system will do in unforeseen situations, as mentioned above. Basically, when you try to automate an entire generation ship, you are essentially trying to replace a human society with a robot society, which
might work better but is even more unknown at present than a stable advanced human society. And again, facts not in evidence: we don't know at this point if it's even possible for a form of intelligence to understand how it works well enough to duplicate it in a new medium. So we don't know if we can create sufficiently strong AI, or have it last long enough for interstellar travel, or maintain its loyalty once we set it loose.
