Why don't you start root canal treatment right away on a tooth whose nerve is still alive?

Because when the nerve is still alive, preserving it as far as possible is better for the life of the tooth. Even if the cavity is close to the nerve, we can first try pulp-preserving treatment, covering and protecting the nerve with a material such as MTA, and then watch how it progresses. We usually monitor for weeks to months, and if during that time 1) sensitivity worsens, 2) it throbs even at rest, or 3) the pain wakes you at night, we switch to root canal treatment.