Did you read that article about how stopping teaches dogs to check in with you? It said constant corrections can make some dogs anxious or stubborn. What worked for you sounds like it builds that patience they talked about.
Maybe it's just me but idk if it's that serious to always correct them right away. My dog figured it out after a few weeks of just stopping when he pulled, and now he walks fine. Quick fixes might work faster but sometimes letting them learn feels less stressful for everyone, you know? Treats and patience go a long way too.