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:

*

*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 

I wouldn't put too much philosophical labor into contemplating the null hypothesis per se, as the OP does.
As I have discussed here, this is a device through which we can determine whether the data allow us to assert probabilistically the direction of influence.
And the direction of influence is a heavyweight, in all worlds.
