It would make more sense to send 10 - 20k frozen embryos that can be grown in a lab.
I think you missed the reasons.
The point is not to have the bodies. A proper mix of genders can produce babies easily enough.
The reason for all the people is the knowledge and experience they bring. You have people who can pick up equipment and immediately be functional. You arrive at the planet and have geologists and biologists and miners and architects and environmentalists who can start to work, coordinators and planners who can manage the projects. People limited to physical sciences tend to overlook other needs, so you need artists and psychologists and people who study aesthetics to provide alternatives to large gray boxes the scientists tend to create. You'll also need entertainment for the people, food beyond "nutritional supplement 24", and so much more.
Even if you bring a bunch of books, there is still much that needs to be learned through experience and there is currently no substitute for it.
I think you are not considering the additional problems, as mentioned in this thread, that a colony sized vessel would bring.
For starters the experienced people who set off from earth would be dead on arrival, their children would only inherit a small percentage of that person skills and the remainder, like today, is learnt through digital media and practice. They too would be dead on arrival and their children would also inherit a small percentage of their skills. There is no guarantee that their children would have any interest in the optional additional curriculum (stuff that will not give them a position of authority on the vessel) or that the resources will be available down the line to teach this. If forced to learn that stuff it is purely a political stance.
A larger ship means more mass, fuel, expense and things that can go wrong. Problems could result in food shortages.
As well as the necessary engineering spaces you will also need in great supply of hospitals, schools, religous areas, sports arenas and many other conventional social spaces which would require many doctors (skilled in a wide range of issues), clerics, teachers, arbitrators, logistics staff - basically an economy of people. Is money as issue?
Is there potential for a disease outbreak?
Survival is significantly more important than bringing people fluent in shakespear. Non critical skills can be developed (and developed in its own unique way rather than a poor copy of earth cultures) over the many generations that they will have together once they make the difficult journey to their destination. And the embryos can be processed in batches, obviously 200 adults could not rear 20,000 babies.