I'm emphasizing that, because of a state capital being half of a paired list in most people's minds, a state capital can be used as a synonym for an entire state, even when it's a small city. So if "Hays" is seen as undesirable because unfamiliar motorists are not likely to associate it with Kansas (and thus the east, coming from Denver), Topeka is a good choice because for people who just need a sign saying "toward Kansas" it means the same thing. At the same time, someone with a specific destination elsewhere in Kansas, like Dodge City, is given the additional information that this route may not be the best route for them, as it heads to a part of the state that they are not interested in visiting.
TLDR: in before someone says 'just sign "Kansas"'