Yes, from a cartographic perspective, limiting place=* to a single value at a time is a challenge. For that matter, some well-designed print maps filter and size places purely based on simple heuristics like population and symbol collision plus a boost for capitals, which skirts the whole idea of data-driven place classification and also has a side benefit of a more intuitive legend.
So there’s an inherent limit to how well we can or would want to fit place classification to cartographic needs. But I figure that, as long as we classify populated places at all, at least it should be predictable enough to serve as an input. Currently it borders on chaos in some places, breeding conflict among mappers, which is no good.
One of my goals with this writeup is to raise awareness that a place=* value isn’t necessarily tied to whether the place shows up at enough zoom levels to be discoverable. I think this misconception is a major source of discontent and a reason for fudging the definitions. Maybe we can solve that problem by simply promoting alternative renderers that surface labels more aggressively, as in the demonstration maps I posted. That could lower the stakes so that even the admittedly simplistic thresholds we had in 2006 would satisfy most mappers.
Interestingly, we’ve had folks from the Plains states express a very different opinion, that for example Casper is a big city on par with the likes of Denver. Maybe from a certain perspective, these words have more to do with a local maximum than an absolute value. With enough coaxing, I think we could find a compromise between these extremes that makes Southern Californians, Midwesterners, and New Englanders equally unhappy. 
This exploration has clarified for me that we need to better distinguish between suburbs and the cities they depend on, rather than relying on a place’s size to communicate that information. Otherwise, a renderer that naïvely categorizes places into buckets by population will get some cities wrong. For example, 90% of the Atlanta urban area’s inhabitants live in suburbs outside the Atlanta city limits, especially in large suburbs like Sandy Springs, which few outside Georgia have ever heard of. Hundreds of cities have only a plurality of the population within the principal or secondary city limits.
As the Census Bureau colorfully illustrates in its history of metropolitan areas, the notion of central and peripheral places has been around longer than central place theory, and laypeople are quite familiar with it intuitively, even if we can’t quite put our finger on a definition. Unfortunately, a suburb is more similar to a place=town than a place=suburb, which is part of the city rather than an adjunct to it.
This is not to say that our place points must comprehensively represent every suburbanite. The Barnstable Town urban area is a classic example of standalone, aimless suburban sprawl. But I think one of the advantages of the approach I explored is that the urban areas often indicate where people self-identify with a larger place. The population of Kirtland, New Mexico, “dropped” by over 90% overnight when the small core of the CDP incorporated in 2015. The outlying residents don’t go by a different name. Their location relative to the town boundary is adequately communicated by the boundary itself, but it would be great if we could somehow gesture at their contribution to the town’s stature in a deterministic way.