As for "nuanced purple maps"---

That kind of map is harder to interpret by non-specialist users (usually, managers, bureaucrats or politicians, who can barely read a map at all). In fact, that is exactly what the density-dot map I also included in my suite does, it gives you a visual cue that it directly correlated to the mapped quantity without breaking it up into distinct finite categories. For this type of data, that is the most precise way of characterizing the distribution. But to the untrained eye it looks messy and incomprehensible, sort of like an omelet. Unless you really know what you're doing, you can't see trends or hidden features easily.

Another technique that can be used is a contour map, which works great for terrain shaped by familiar natural forces, but fails perceptually for random, discrete data. But contouring requires a great deal of interpretation and interpolation, and an intimate knowledge of the process which creates the landform. Software can contour discrete data points, but it never looks as good or as realistic as that done by hand. I worked for five years drawing contours on air-photo relief maps. Software just can't do what even the clumsiest human operator can.

Another disadvantage of the continuous gradation map is that the data is sampled, that is, we had a database telling how many people lived in each TAZ, but we didn't know where each person lived in that TAZ, and there were too many to map them all. Even with density dots, you have to pick a value (I chose 200 people/dot) so that populous areas of the map didn't merge into an undifferentiated mass of clumped dots, like snail eggs.

Another problem is that since the data is sampled, as you cross TAZ boundaries, the density may change drastically, but not necessarily at the boundary (which is why dots are placed at random within a TAZ). This will cause linear features like TAZ boundaries to appear in the gradated coloration you use. Seeing a clearly artificial straight line in a continuous natural distribution is very distracting and confusing. It looks like you are either making something up, or your data is discontinuous and erratic. (As all data is, at some level of resolution).

When making maps for policy makers and citizens, the cartographer isn't just concerned with the highest possible accuracy and precision, but also with communicating the data in such a way that it displays what's really going on on the ground.
The data analysis capability of the human visual system, and the sophistication of the user likely to be using that product must be considered, which means subjective decisions must be made by the geographer in order to create as truthful a representation of reality as possible. What you leave out is as critical as what you leave in. USGS Quad sheets and UK Ordnance Survey maps are excellent examples of first-rate cartography, but those are not thematic maps. They display physical features, not statistical quantities.

Software can give you tools to do this, but map making is an art. Experience, training, instinct and talent play an enormous role. And if you have an agenda, even an unrecognized one (most people are inherently honest) it can show up. For the professional propagandist, on the other hand, cherry picking, taking facts out of context, and all the other tricks of the paid liar are also available to the cartographer. There is no such thing as totally objective data. Interpretation, analysis, professional consensus, biases (both deliberate and hidden) and social and psychological considerations all play a role.