I think under the definition of CBT of the study that peaigr mentions peirce, he's already engaging in CBT when doing his exposure therapy.

The study also says:

Specific therapy techniques, such as exposure and cognitive restructuring, were not associated with higher effect sizes. However, given the substantial heterogeneity in the samples and treatment approaches used in the studies, it is difficult to make firm conclusions about the relative efficacy of different CBT techniques.

It basically provides no evidence that seeking a professional has an effect that's better than what peirce is already doing.

Furthermore the study is about raising the confidence of people who have a low baseline and peirce says that he already has an above average baseline.

The studies also seem to be measuring decreased social anxiety as a goal and don't measure the outcome of successful social interactions.