Why do capacitor datasheets avoid directly giving the ESR value?
It's just one of many ways to specify the same thing.

Other ways include:


dissipation factor (DF)
quality factor (Q)


$$ \tan \delta = \text{DF} = {1\over Q} = {\text{ESR} \over X_C} $$

It's simply a matter of which is more convenient for the task at hand. The choice of which measure is used might be influenced by the expected application of the capacitor, or just tradition.

Notice in particular that the term including ESR also includes the capacitor's reactance, which is frequency dependent. Thus, to calculate the ESR from the loss tangent, quality factor, or dissipation factor, we must also know the capacitance and the frequency at which these other measures are specified.

Furthermore, although the ESR model would suggest a resistive loss independent of frequency, in reality the ESR also varies with frequency. Thus, it is unwise to extrapolate any qualities given in the datasheet to substantially different frequencies.