Counting and measuring is frequently done because it can be done, with at least some awareness that it is not in fact adequately characterizing what one seeks to "measure", nor serving the purposes for which measurement is being undertaken.
Despite which, people feel obligated to count/measure because .... they lack awareness of any alternative?
Numbers and counting, together with mathematics, have played and will continue to play a valuable role in human cultural development. Among other things, they can facilitate the exploration and discovery of commonalities between individual perspectives, provide a solid foundation for establishing the lack of validity of otherwise accepted understandings, and open new horizons of possibility that would be difficult or impossible to reach any other way (cf Figure 2).
The usefulness of numbers, counting, and mathematics derives from the effort of conscious brain processes to achieve single, coherent, and readily assailable understandings, and the distinctive kind of information processing that has evolved to achieve that style of understanding (cf The Magical Number Seven, Plus or Minus Two: Some Limitations on Our Capacity for Information Processing).
While useful, neither numbers nor counting are essential to this form of brain processing, as evident both from common experience and from such instances of "qualitative" science as the elaboration of a theory of evolution, the characterization of behavior as depending largely on unconscious brain processes, and Godel's proof. The latter is particularly interesting in that it clearly sets well-defined limits on what can be achieved by "formal processes" of the sort that are represented by counting, measurement, and mathematics, and which seem to be the primary way in which conscious brain processes handle information.
Humans are also equipped with a different, equally distinctive style kind of brain processing that demonstrably works better in many cases, particularly those with larger number of variables and more complex patterns of causal interaction (cf. Figure 3). This unconscious set of brain processes (Figure 1) also appears to be more directly concerned with "value".
Without denying the value of numbers, counting, and mathematics in either science or the conduct of human affairs generally, one can quite legitimately challenge the priority given to them in particular cases. It seems likely that this priority reflects some combination of a misguided search for security and certainty, and an effort by people comfortable with and/or inclined to numbers and counting to exert and sustain control over those less comfortable with or inclined to numbers and counting. In neither case ought a presumption that "What counts is counting and the products of counting" be allowed to go unchallenged. There are alternatives, both in conscious and in unconscious processes. The challenge is to match the distinctive kinds of information processing styles to the needs of the task at hand.
Creative rationality (supported by conscious brain processes) exists productively in the absence of numbers, counting, mathematics. There is both quantitative and qualitative professional science, so regarding numbers/counting/mathematics as a requirement for those interested in doing science is an unnecessary and undesirable limitation on individual aspiration as well as on the diversity of perspectives on which science fundamentally depends (cf an exchange between a chemist and a biologist, and "A Vision of Science and Science Education in the 21st Century".
The belief that there is no alternative to numbers/counting/mathematics in dealing with any meaningful array of challenges is simply wrong. The brain has a set of "unconscious" processes that are demonstrably more effective than conscious processing at dealing with situations involving large numbers of complexly inter-related variables. This capacity needs to be better appreciated as an available alternative in cases where numbers/counting/mathematics are know to be inappropriate/ineffective and, more generally, more clearly acknowledge and supported as an essential part of the intellectual enterprise and capability to think productively and creatively.
There is an interesting and entirely open issue as to whether mathematical descriptions are the most appropriate/fundamental ways to characterize "reality", or whether they are instead useful but transient stages in still more mature forms of description (see an exchange between a physicist and a biologist).