Why would exploratory data analysis be important to undertake before null-hypothesis tests?
It is often necessary to know a little about the system being explored before sensible hypotheses come to mind and it is very useful to know about the variation and noise in an assay prior to designing an experiment. Exploratory experiments and analyses are good for that. Don't be too quick to decide that a dataset is definitive.
Of course, you should know that hypotheses that are suggested by the data in exploratory analyses will have a high chance of giving you a spurious 'significant' result if you test them using the same data, so ideally the exploratory analyses lead to the design and running of new experiments to specifically test hypotheses.
There really aren't rules on which comes first: data-driven (hypothesis-generating) analyses then hypothesis-driven analyses, or hypothesis-driven followed by data-driven.
If you knowingly want to test hypotheses and then do knowledge discovery, then you can answer questions you have, and then learn from (data-driven analyses) a part of the data that is novel (never been studied before) in order to generate hypotheses.
Otherwise, if you needed to run exploratory first to generate hypotheses, then if nothing is found -- no patterns, no clusters, no correlations -- essentially noise, then you wouldn't be able to test any hypothesis since they wouldn't exist.