This is dependent upon jurisdiction; some areas it may not be required, while others it may be. I've been involved as a Club Instructor for 45 years. I list the club as a named insured with instructor liability insurance. In other words, if I (or the Club) gets sued as a result of a training accident, they are covered. This doesn't however cover other club dives or activities. I suspect that most pools are insured and the pool owner has a liability insurance policy which may include those who contract time with the facility (something to look into).
Generally speaking, the Board of most non-profit corporations don't have a high risk of liability. Because of this insurance isn't expensive. That said, every club I've been involved with has a liability policy. As the risk is low, so is the premium. If it allows the Board to sleep better; it's a good investment.