Actually, there are three different "Rule of 3's" and all three of them are important to anyone who works in Fire/Rescue or EMS.
The first one is espoused by survivalists. It goes something like this:
You can survive 3 minutes without air, 3 days without water, and 3 weeks without food.
While not exact, that Rule is pretty close to reality for the average human. I know that I can hold my breath for a little more than 3 minutes, but it's pretty uncomfortable after about a minute, it's VERY uncomfortable after two minutes, and at three minutes, it's agony. I've never gone even one day without hydrating, nor more than about 30 hours without food. I hope I never have to do either one.
The second Rule of 3's is the Cave Diver's Rule, now adapted for firefighting as the Rule of Air Management. This Rule states that you use 1/3 of your air to enter the hazard area and do whatever task you planned to do, use 1/3 of your air to exit to a safe atmosphere, and 1/3 of your air for emergencies. It's a good rule and following it has saved the lives of divers, firefighters, and confined space rescuers.
The third Rule of 3's is my rule - "Waller's Rule of Leadership Change". When an organization has a leadership change at the top, there are generally three possible results for the organization including changes in organizational effectiveness, the training cycle, and morale. The three possibilities are that there will be no real change. In that case, the organizational effectiveness, training cycle, and morale tend to continue at the same levels, in the same manner, and with similar results as what took place prior to the leadership change.
The second option is that the new leader may demand big changes and that the changes are improvements. That typically means that the organization will become more effective - at some point. That may take time, and that is dependent upon the nature and complexity of the changes, the amount of training required to adapt to the changes, and how the changes and the training cycle affect morale.
The third - and worst - option is that the new leader may demand big changes and that the changes are bad ones, or even disasters. This change type can destroy organizational effectiveness, drive good people out of the organization, trash the training cycle by requiring constant basic training for new people rather than more advanced training for the more experienced employees, and concurrently ruining morale.
How leadership change is handled is primarily the responsibility of the new leader. The new leader will likely have some constraints. After all, everyone has a boss. If the leader has the power to throw off contraints, that can be either very good or very bad for the organization and for morale.
Hopefully, the next leadership change your organization has will be the kind that improves organizational effectiveness, takes the training cycle's requirement into account, and solidifies and improves morale.
After all, happy employees will work harder for the new leader. If the new leader has a vision, can sell it to his/her boss and the troops, gets everyone's buy-in, and uses it to improve both the organization and morale, he/she is likely to be successful. One caution for new leaders here; sometimes the organization is doing fine, and the best you can do is to be a caretaker for that success until an opportunity for improvement comes along. Don't force change on the organization simply for change's sake. If you do, you've eliminated 1/3 of the possible outcomes, and now you're down to a 50/50 chance for success. Those aren't good odds, and the troops may feel as if they've been without air for a lot longer than three minutes.