How is it a strawman?
You are not allowed to have children. The population has to be carefully controlled. How exactly do you plan to enforce that? Forced sterilization? Forced abortion?
Also, since it's a closed system, any child born is replacing an adult who has died. So when Bob the Engineer dies, Suzie gets to be born and she has zero choice. She must become an engineer. She can't be a botanist because we already have those. She can't start her own business, because the ship requires an engineer. So, from birth, Suzie is chosen to be the next engineer to replace Bob, that's the only education she is allowed. Because it would be a waste of resources to train her for anything else and the ship cannot afford to waste resources.
Which, of course, brings up another elephant in the room. Exactly when does Bob the Engineer die? Once he is too old to work, does he get to take a long walk out an airlock? How exactly do we care for our elderly and infirm in a system with tight population caps and virtually no extra resources? It's not like we have space for those who cannot contribute to the function of the ship. So, are we recycling Bob on his 65th birthday? When would retirement age be anyway? Can I retire early?
Oh, right, I can't quit. Somehow I'm not a slave, but, I cannot choose my job and I can never, ever quit my job. But, I'm not a slave, apparently. Because you cannot have institutional slavery apparently. Slaves must be owned by someone to be a slave.
So, @ Shasarak, how do you deal with people who want to change vocations?
It is a strawman because your plan just does not work. Why would you have a set capacity of, just for an example, 100 people on your ship and then start with the maximum population already on board? That would mean that you have to wait for someone to die before having any children to "replace" them. Which means that for the next 15 to 20 years or so you are having to some how get by without someone that you really really needed.
And likewise for machinery, why would you be operating at 100% capacity all of the time? How do you maintain something if you literally can not turn it off without killing everyone on board? I mean I am not an Engineer and even I can see that would be a badly designed ship to try and travel 1000 years in.
Population control is not hard we have it now, it is called the contraceptive. The largest country on earth practises a pretty extreme version of it right now. The best way to deal with population control would be through a social agreement with exceptions built in to take into account those people who dont want to or are not able to have children.
And as for forced job assignment, would you personally want to be traveling through space in a ship that is maintained by who ever is born into the Engineering class or would you prefer that position to be filled by the person who is best qualified? Hereditary systems dont work on Earth so why would you try it on a Generation ship?
So that is why I think that your whole proposal can be summed up as a Strawman, something that is set up because it is easier to defeat than a real argument.