Why are standard frequentist hypotheses so uninteresting? In almost any textbook introducing the topic of frequentist statistics, null hypotheses of the form $H_0: \mu=\mu_0$ or similar are presented (the coin is unbiased, two measurement devices have identical behavior, etc.). Classic statistical tests such as the $Z$ or $T$ tests are then based on rejecting these null hypotheses.
As I see it, these types of equality hypotheses are uninteresting for a number of reasons:

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*In "real life" one is always only interested in some finite accuracy $\epsilon$, meaning the hypothesis of interest is actually of the form $H_0: |\mu-\mu_0|<\epsilon$.

*The equality hypothesis is a priori known to be wrong when considering continuous variables (no coin is perfectly unbiased in reality!), and as a corollary,

*The fact that the null hypothesis cannot be rejected is by definition temporary, and is an artifact of not enough data. Given enough data, any type of equality hypothesis on continuous variables will be rejected in a real world use case.

So, why are these hypotheses still used, both in text books and in applications, while it is difficult to find formulas for more interesting* "real" hypotheses?

* e.g. a question I recently asked regarding these types of hypotheses 

The appeal of such hypotheses lies in their simplicity and the analytical tractability (or just simplicity) of testing them.*


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*In "real life" one is always only interested in some finite accuracy $\epsilon$, meaning the hypothesis of interest is actually of the form $H_0: |\mu-\mu_0|<\epsilon$.


This might be true for continuous phenomena, but not for discrete ones. E.g. in genetics a gene either has an effect on something or not. (I guess there can be even better examples than that.)

The fact that the null hypothesis cannot be rejected is by definition temporary, and is an artifact of not enough data. Given enough data, any type of equality hypothesis on continuous variables will be rejected in a real world use case.

Again, this holds for continuous phenomena only.
What we can criticize is perhaps the choice of examples in textbooks. Perhaps more examples of discrete phenomena are in order.
*Your criticism could just as well be directed at statistical models. These are often quite simple (e.g. the ubiquitous linear models), and much of their appeal is also in their tractability and simplicity of interpretation. Or even models in general, as again they are simplifications of reality with all of the drawbacks (but also benefits) that come with that.
