Most analytical techniques use a calibration curve.  There are a number of advantages to this approach.  First, the calibration curve provides a reliable way to calculate the uncertainty of the concentration calculated from the calibration curve (using the statistics of the least squares line fit to the data).
Second, the calibration curve provides data on an empirical relationship.  The mechanism for the instrument's response to the analyte may be predicted or understood according to some theoretical model, but most such models have limited value for real samples. (Instrumental response is usually highly dependent on the condition of the analyte, solvents used and impurities it may contain; it could also be affected by external factors such as pressure and temperature.)
Many theoretical relationships, such as fluorescence, require the determination of an instrumental constant anyway, by analysis of one or more reference standards; a calibration curve is a convenient extension of this approach.  The calibration curve for a particular analyte in a particular (type of) sample provides the empirical relationship needed for those particular measurements.
The chief disadvantages are (1) that the standards require a supply of the analyte material, preferably of high purity and in known concentration, and (2) that the standards and the unknown are in the same matrix. Some analytes - e.g., particular proteins - are extremely difficult to obtain pure in sufficient quantity. Other analytes are often in complex matrices, e.g., heavy metals in pond water. In this case, the matrix may interfere with or attenuate the signal of the analyte. Therefore, a comparison between the standards (which contain no interfering compounds) and the unknown is not possible. The method of standard addition is a way to handle such a situation.