Baxter's mailman barking is almost gone after my clicker experiment, but a pro trainer friend doubts it.

My Beagle Baxter would lose his mind barking at the mail carrier every single day, and I was at my wit's end! I got a clicker and started rewarding him the moment he stopped barking, even for a breath. After a few weeks, he barely makes a peep when the mail arrives, which thrills me! However, my professional dog trainer friend says this approach might just mask the problem and not help Baxter feel calm, worrying he could become anxious from holding back. Now I'm second-guessing my whole method. I'd love to hear what you all have to say. Is it better to stop the barking fast or focus on the root cause?