Data driven priors are more common now. Sometimes this is called empirical Bayes. Also priors can change after model checking. These are data driven priors, but

Data driven priors are more common now. Sometimes this is called empirical Bayes. Also priors can change after model checking. These are data driven priors, but not EB. The prior is only negligible in infinite sample sizes. It could still have a large effect given 100s or 1000s of observations. For example, if the prior variance is miss specified by an order of magnitude (not uncommon).