Consider: it will eventually be possible to replace every part of a person with new biology. It will be possible to replace all component pieces
No that is ludicrous, biology is shaped by possible path-ways it can grow into. For example birds cannot grow jet-turbines even if there were kerosene berries, because the spinning part of the turbine would be detached and would need to be a semi independent life form.
To an extend there is molecular machinery operating at the lower levels where you can plug out components and switch them for better stuff, this will be a boon for health-care or better yet sick-prevention-care. However a lot of stuff in biology is ridiculously interdependent and multifunctional. On top of that is that biology is not independent from environment, so you have to take a phenotypical view where the biological function of your body will vary based on environmental inputs about as much as it depends on the components.
There is some room for some optimization, you probably can ad an avian lung inspired breathing system for higher oxygen supply efficiency, and do stuff like make vascular-system contract and expand in a travelling wave motion to move blood more effectively and also function in a way to be a redundancy for the heart and prevent bleeding out in case of injury. Obviously you'd want to be able to do photosynthesis in your skin, and have zoom lenses in your eyes as well as have a wider spectrum light sensitivity. But these are sort of the easy dials you can turn. Consider that a lot of the stuff related to intelligence and behaviour is collective in nature, where you start to manipulate a system that has the bodies of multiple people as components. This is opening a can of worms, because now you are designing people to have different but complementary biology, that also responds to the environment.
The poor, the criminal, the “worthless”, these people soak huge amounts of resources as society tries to make something of them.
Your conceptual idea of fixing the worthless people, is based on a one sided view where you want to adapt people to fit in what ever way you measure worth, and you have to consider what system you want to change, it might be easier to modify the surroundings of people than to modify people.
Economics rules the world. Science will squish the differences between people sooner or later.
Well maybe there will be a sort of coalescing to standard body, but it is likely that after this it will be something like a basis for diverging developments quite possible forced by space travel.
We also have to account for the limitations of genetic editing, which only acts in a very limited way, and spurs fears of changing the genetic basis for humanity that seems to be somehow tied into some deep-rooted fears about essence of self. It might be easier to add modifiers that reconfigure biology on various non genetic levels of the body that are not permanent, much more versatile, and a lot cheaper to manage, because it's not trapped in organic pathways as much.
Consider that making everybody have the same body and as you say squish all differences might not lead to more equality. Because right know we have enormous inequality and class stratification that is not related to the bodies of people at all. Consider that the tendency of generating inequalities based on bodies could be more effectively-countered when people with different biological nature, can have modifiers that allows them to negate differences that are the basis for discrimination more effectively. Consider that the ideas that arise from breeding stock and traits of individuals are unlikely to be effective models since they predate science and had their utility for modelling reality in terms of attempting to optimize combining breading partners to produce offspring of organisms towards narrow goals for "utility animals/plants" With the tools that are being developed now and in the future will not have the same tendencies and produce new patterns.