But I don't really understand why the boundaries are curved. Natural features still make more sense in my opinion, but ignoring that, why not focus more on lines of longitude and latitude? Perhaps some straight diagonals.
I think the idea is to not use natural features (e.g. river) or arbitrary straight lines, but instead to divide the country with only regard for population, metro areas, and local culture, and also to try to make the states more equal to each other (in both population and land area). One big idea with the map is to eliminate any case where a metro area (e.g. NYC, Louisville KY, Portland OR) spans a state boundary, and instead keep the metro areas well within states, and only have the borders drawn through areas as rural as possible. This keeps local culture together, and avoids things like large numbers of people commuting from one state to another (very, very common here in NJ, both near Philly and NYC), and having to deal with paying taxes to both. Rivers aren't necessarily great borders from this point-of-view, thanks to bridges and tunnels.
This map was made by a college class in the mid-70s; I imagine they got a basic map of the US and highlighted all the population centers, wrote in their populations, then debated which ones went together, and drew borders around them so that the borders were as far from the population centers as practical. Straight lines (at least like the western states have, drawn along parallels) would probably end up going through a lot of population centers. I guess you could try drawing more complex polygons, rather than curvy lines; it'd certainly be easier for the surveyors to deal with polygons than curves.
32 states sounds like a good number to me: that's 2^5. They could give up on the equalized land area idea and make Alaska a single state again.