I think this depends on the field. In physics and engineering, there is a body of underlying theory from which one can derive a hypothesis, based on some causal mechanism, before seeing any data. You can then go out and collect some data to confirm - in many cases this is basically just a sanity check, occasionally the data is in conflict with the underlying theory and you learn something big.
Outside of the hard sciences, your procedure could make more sense. We do this in business consulting (not always a science but it can be if you do it well) by looking through financial, operational and HR data and asking questions or trying to draw out interesting relationships that can lead to hypothesis for deeper examination. I would expect the same is true in lots of health science as well or any empirical field where we have data on outcomes and the characteristics that may influence then. Even in these fields though, it doesn't preclude starting with a causal mechanism based on underlying theory and then devising data collection and experiments to go out and conform or refute your hypothesis.
Personally, I've seen lots of cases where people are quick to rely on statistics and empirical studies, without looking for the mechanism that must exist behind the relationship they're claiming. Such findings are much weaker than results that may have less data or a bigger p-value but are grounded in actual theory and not just reporting a model-free relationship.
So to summarize, there is certainly a place for the order you suggest, but if done right, a stronger formulation can be made based on what you call the American school system method.