If the IQ-mutation load hypothesis[1] is true, the sea of slums problem will be taken care of by trivial genetic engineering. Smart people with good software are pretty good at entertaining themselves and making do with basic resources.
[1] The hypothesis is that the baseline human genome encodes a master race, but has been spoiled by a handful of mutations. Fix the mutations with "simple" proofreading and out pops a race of handsome, athletic geniuses.
Hi! Genetic engineer here. Your idea of "trivial" is weird: we have no way to replace chromosomes, or even edit them. All we know how to do is add things.
The idea is fascinating: although you're getting downvoted for saying "master race", the notion that the vast majority of random mutations are "bad" while the DNA we hold in common is "good" holds a lot of water. We have no idea how to edit our own DNA, however. We simply can't do it yet.
Trivial in the sense that it would cost on the close order of $10 billion to figure it out, and the rewards would be in the $100s of trillions.
Trivial also in the sense that the general path to proofreading DNA is "obvious". Make a DNA segment that aligns upstream of the mutation. Glue a dicing enzyme to one end. This breaks the chromosome upstream of the mutation. Repeat for the downstream side, chopping out the mutation. Then incubate with the correct sequence and DNA repair enzymes. Voila, the mutation is repaired. This is nearly off the shelf. The not off the shelf part will be getting methylation and histone packing to come out right, otherwise you get subtle but appalling birth defects.
[1] The hypothesis is that the baseline human genome encodes a master race, but has been spoiled by a handful of mutations. Fix the mutations with "simple" proofreading and out pops a race of handsome, athletic geniuses.