Well, for one thing it doesn't carry that subconscious bias of interpreting something below 0.05 as guaranteed significant as people tend to do with p-values, b

Well, for one thing it doesn't carry that subconscious bias of interpreting something below 0.05 as guaranteed significant as people tend to do with p-values, but is a softer metric that reflects your belief in one or the other hypothesis, given the data. I think that in itself makes it easier to evaluate and reason about. The fact that you can incorporate (and reflect on) a priori assumptions about the likelihood of one or the other model is another advantage imho.