I see nothing in what you are describing that indicates he cares or gets it at all. People can be flaky about emails. But a therapist should not be flaky about anything. You are paying them to be responsive and professional, and to be consistent and predictable. Being busy is not an answer, it's an excuse. He needs to make clear his policy on email and then stick to it. And his policy should be driven by what is best for the clients, not by his schedule and obligations. He sounds like an idiot.