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 

No model is ever true. This means that not only the null hypothesis is not true, neither is the alternative, nor something like $|\mu_1-\mu_2|<\epsilon$. If you're interested in which model is true, you're generally lost in model-based statistics; there's nothing particularly wrong about standard null hypotheses. Whether the $H_0$ or any parametric model is true is simply the wrong question.
Of course you can decide yourself what you're interested in, but I find often informative whether or not data give any evidence against a simplistic random variation "nothing meaningful is going on" model. Of course we all know that non-rejection doesn't mean the null model is true, but if you can't reject it you should really really really not claim that the data show anything meaningful, and by the way then of course you can't reject $|\mu_1-\mu_2|<\epsilon$ either, whatever $\epsilon$.
Of course you should be interested in effect sizes and not only run a null hypothesis test, so that even in case your point null is not rejected you can see whether data are still compatible with a ridiculously low effect (i.e., compute a confidence interval and see whether something as small as $\epsilon$ is in it, in case you can specify a "critical $\epsilon$").
Baseline: What's "interesting" is subjective, but the rationale of testing a point null is not the question whether it's true (it isn't, but it isn't alone at that), but rather whether there's any clear "signal" in the data deviating from it. In case there is, you've got to do more to learn more.
Note particularly that it is one thing to actually reject the $H_0$, but quite another to just claim, in case you didn't reject it, that you'd have rejected it with more data. Particularly then you won't have any idea in which direction things will go. And also, D. Mayo made the valid point that if rejecting a $H_0$ were so easy indeed, why is it often so hard to replicate rejections?
Another consideration is that in fact tests will not always reject a false null hypothesis with a large enough data set, because (a) many standard frequentist tests are one sided and with a large data set things may go to the wrong side, and (b) in case the nominal model is wrong (which it always is), one can in many cases even find other models that imply a low probability to reject the null hypothesis for a range of parameters and also for big data sets, for example if you use a t-test and the true underlying distribution has very heavy tails and/or produces outliers, or if you have negative correlation between observations.
