As is the case with most injury prevention research, it is difficult to distill injuries down to a single causative factor. This systematic review and meta-analysis looks at a single common running variable (step rate) and multiple outcomes (injuries, performance, and biomechanics).
Step rate is often one of the first targets for coaches and clinicians as it leads to a cascade of changes (step length, impact pattern, loading rate, and magnitude). As with any running change, it comes with a cost. Changes in running technique reduce (no matter what the change is) running efficiency in the short term. If not taken into account, this could cause frustration and over-training, potentially leading to injury. If looking strictly at the change in step rate on biomechanical factors, there is reason to believe it could result in injury reduction. However, outcome data at this time does not support that conclusion. This review doesn't change our current conclusions.
The MA and SR included 37 papers and they found increasing the set rate either reduces or doesn't change kinetic, kinematic, and loading variables. There is little data on preventing running injuries, pain management, or performance. What we do have suggests step rate does not influence injury or pain while it may have a detrimental effect on subjective measures of performance. You are likely better off focusing on fitness level, training and lifestyle habits, and psychosocial factors than running mechanics.