People use "the chatbot from OpenAI" because that's what became famous and got all the world a taste of AI (my dad is on that bandwagon, for instance). There is absolutely no way my dad is going to sign up for an Anthropic account and start making API calls to their LLM.
But I agree that it's a weak moat, if OpenAI were to disappear, I could just tell my dad to use "this same thing but from Google" and he'd switch without thinking much about it.