Well, they are good for lots of things. As indicated, they are part of Wyoming's heritage and as such warrant recognition. Humans have developed anthropocentric views that simply fail to hold water in the overall scheme of things. Many Wyoming residents have perfected this trait by viewing the whole world as revolving around a sparsely populated state and feeling that their own personal greed should be placed above the good of the nation and benefits to the general public. If you don't subscribe to the argument so far, read on.
Nongame fish are environmental indicators or barometers of larger systems.
Consider, for example, that the longnose suckers and creek chubs in your nearby stream suddenly die en masse. You would likely be concerned that something is wrong with the water. This actually happens and people get quite upset. The phone rings and the caller is concerned for his health, the health of livestock, birds, mammals, and sometimes even the fish. On a broader scale, nongame fish can be indicators of the status of and changes in common and unique water systems.