Why can't be hypothesis testing done in opposite way? When doing hypothesis testing, we calculate the distribution of test statistic (for example z) under null hypothesis and then compare the actual z (one calculated from our data) to it.
Why can't we instead calculate the distribution of z statistic from our data (by bootstraping mean, for example) (or calculate 95% CI) and compare it to 0, like it is shown below.
I'd also see an example (or a simulation) where this fails, not just a theory behind it.


The logic of hypothesis tests asks whether what is observed is plausible under the null model. This requires that probabilities are computed assuming the null model.
If you take the parameter value estimated from the data and then compute the probability for 0 or something further away (which is how I interpret your suggestion), you basically compute whether it would have been plausible to observe an estimated value of 0 given the assumed parameter value that is actually the estimated one. This doesn't make sense to me - why would you want to compute the probability for observing zero (or rather a certain set involving zero) if zero is not what you in fact observed as estimator? (Although your suggestion may be in some cases equivalent to doing something reasonable, see answer by Sextus Empiricus.)
