The future is still in the future
I just did a project with a work experience student that involved looking back through four top medical journals for the past year (NEJM, JAMA, Lancet and BMJ), looking for reports of randomised trials. As you can imagine, there were quite a lot - I'm not sure exactly how many because only a subset were eligible for the study we were doing. We found 89 eligible for our study, so there were probably at least 200 in total.
Of all those trials, I saw only ONE that used Bayesian statistical methods. The rest were still doing all the old stuff with null hypotheses and significance testing.