My uncle was awarded a PhD in the late 1970's from Arizona for the technical papers on generations ship written for NASA, so I have some insight to this stuff [0].
The TLDR; for the project was that assholes suck. Many many things are hard to work out for a generation ship, from the correct number of light bulbs to bring with you, to the plumbing, to the risks of permanent 0g. In all, the engineering was remotely possible for the tech at the time, but extreme. A generation ship, ala a giant metal can with people and pipes in it, was engineeringly feasible, but the human considerations made it impossible.
The main issue was that the ship's inhabitants were to be born, essentially, in Alcatraz; a prison they could never escape. As time went on, the crew was expected to become less and less aware of the danger of the vacuum and an accident was exponentially likely to occur. Most highly isolated peoples, like on Rapa Nui or Naval ships, were brutally strict. As teenagers are wont to be boundaries testers, it was expected they would be the most risk to the ship. Add in deteriorating conditions and failure of parts, and you end up with the Stanford Prison Experiment[2] for generations. The project was a human rights nightmare. For thousands of years, potentially, you breed and die in what may eventually amount to a Nazi death camp.
The simplest solution was to make a giant Stanford torus [1] with the land area of between California or Maryland, stick an artificial sun in the center for light and heat, and launch it at your target [3]. Remove any computers or guidance of the Tube, just let gravity somehow guide you into the right place. Oh and make it big enough that some wacko death cult that may arise can't break it apart or kill everyone. Essentially, you launch a mini-Earth Tube, and let them fend for themselves. When the Tube gets into position, you hope they get curious enough to figure out a way to jump out.
Obviously, the mass of the thing alone is too much to begin to think about, let alone the time it would take to create, launch, fly out, orbitally park and decelerate, and finally disembark. Even back in the 1970's, they knew that the rate of tech increase would just make it so that you launch a robot with some zygotes and grow the people when you get there.
In the end, the possibility of a generation ship was deemed too remote to devote more funds towards. Our better natures think that we could live in harmony in the stars, but history tells us that our darker selves always arise. The issue with a generation ship of humans is not the ship, but the crew, as a lot of the time people can be nothing more than assholes.
[0] By awarded, I mean he published the papers, and someone at UA forced him to take a single class for the requirements, so impressed they were at the scholarship.
[1]https://en.wikipedia.org/wiki/Stanford_torus
[2]http://www.prisonexp.org/
[3]https://en.wikipedia.org/wiki/The_Book_of_the_Long_Sun