If I might add my two cents.
A generational ship has some serious problems.
-Despots / Tyranny
You might wonder why this would be a problem, but so long as people are people there is ALWAYS going to be an idiot with too much power and too little sensibility. In this case it would be anyone in the Captains / Bridges seat. Because much like the overseer in Fallout, this person would have complete control of the ship…Along with all its other functions.
Critical functions such as Life support, air control, Heating (In space the biggest problem Nasa has isn’t the fact that the astronauts might freeze but rather that without anywhere / or thing to cool the ship down the engines would cook the people on board.) Cooling (Plus the very real problem of being exposed to the vacuum of space is not fun, though you can live up to 10 mins in the vacuum of space…But your eyes will freeze, melt, freeze and melt…so fun.), Gravity, and many many more would be under the control of one or more people…Which effectively makes everyone on-board completely at the mercy of whoever s sitting in the captains chair.
And thats without getting into the problem of deciding who the Captain would be after the first 80 or so years…After all the caps son might want to be king now.
Mental illness breeds like a plague in a enclosed environment
-Diseases and Immuno compromised individuals
Living in a sterilised environment seriously weakens ones immune system (Plus Zero G causes steady degradation of the human body.), but here’s the kicker, we could NEVER fully remove all the bacteria and viruses in the general environment yet alone on ones person prior to launching the ship…
So there’s going to be bugs, (And the effects of space, such as radiation and zero g makes bacteria and viruses way more deadly…Plus it makes real bugs even bigger, just look up the Russian Cockroaches. So people are going to be stuck on a ship with limited medical supplies, and even more limited space, in close contact with everyone else…While everyone in the best situation only has a slightly weakened immune system and no other complications, with essentially super bugs.
-The lost / degradation of knowledge.
Every time without fail that a civilisation breaks itself off from the outside world (Be that as a result of geographical factors such as continental drift, or the closure of borders between nation states.), like the separation of Tasmania from mainland Australia with the flooding of the Bas Straight, or a more recent example such as North Korea. The nation / State inevitably suffers a lack of progression, and even the loss of once held knowledge.
This process will be further pronounced due to the ELE that humanity just faced, so a lot of fringe knowledge will have been lost due to the excessive loss of life (Stuff that people may not find to be useful, or mainstream that has taken centuries to develop.) But more worryingly will be the ever increasing chance of critical knowledge loss…Equipment failure losing stored information, or someone deleting it for power (After all such knowledge / skill would be worth more than its weight in modules, and if your one of the only people that know than…) or simply Mechanics and engineers dying or not teaching new students. And one has to remember that the Pilots, Mechanics, Engineers and Doctors have to not forget critical information / become less competent for over 1200 years, while avoiding the pit falls of developing society on board the ship, Despotic Captains with the literal power of life and death on the ship, Equipment failure, information loss, the deaths of Older/ more experienced Mechanics and engineers, resource shortages, emergencies (Disease outbreaks in space are far more lethal due to the close quarters everyone shares and the fact that radiation and gravity can and will make viruses more lethal, feuds like the one that formed in the promotion material and the fact that isolation and close quarters makes people go really crazy…Really fast.