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 

You have to crawl before you walk, and simple examples like testing a coin for bias, under a null hypothesis of zero bias, make for a teachable example for complete beginners (which every single one of us was at one point).
Jumping straight to, say, equivalence testing without even discussing easier null hypothesis significance testing seems like poor pedagogy. Where the majority of statistics education seems to suffer is when it comes to teaching the numerous limitations of hypothesis testing. After all, the OP is right: we basically always know the null hypothesis to be at least a little bit false, and we probably are more interested in something along the lines of $H_0: \vert \mu_1-\mu_2\vert<\epsilon$. Better integration of equivalence testing like this into early statistics curricula is an interesting idea—at least after some basics are covered.
