There are several factors of adding fish that should be considered:
1. By adding over time in the proper order, less aggressive fish may become established before adding more aggressive fish so the more aggressive fish do not dominate the territory before more peaceful fish are added. This can be mitigated somewhat when fish are added together, since all fish will be establishing new territory at the same time, but this can still lead to bigger/more aggressive fish harassing smaller/more peaceful fish during this power struggle since the peaceful fish will not already be emboldened by their own established territory.
2. Adding fish over time allows for mitigated risk on the system should issues arise. If all fish are added at once and a catastrophe results from some unlearned or unexpected cause, all fish are at risk rather than only a few. There will always be risk, but patience allows for more time to prove stable conditions rather than risking all at once.
3. For the nitrogen cycle specifically, adding over time allows for extra security in the amount of nitrifying bacteria to be sufficient or grow sufficiently to control the ammonia load. This may already be sufficient on real live rock, but it is difficult to measure exactly and risks are mitigated if fish are added over time rather than all at once.
4. Adding fish over time also allows for more time for experience/education with lower risk. Though this will not reduce risks to zero, the more experience/education you have, the better your chances should be for success.
5. Adding fish over time also allows for more time to establish maintenance routines on your system that should help toward long-term stability rather than running risks from lack of maintenance with all fish added. The routines will need to be modified slightly as the system changes with each addition, but it is better to have a grasp on the basic maintenance before you have many lives at risk.
There is probably more that I could add and my experiences are still only from a few years in the hobby, but these considerations should be helpful for you.