Here are 3 key points which explain why keeping your rest periods to the prescribed number is so important, and how it will slow your progress down if you fail to do so.
1. Energy Systems
The intensity, workload, and rest you take between sets will dictate which energy systems come into play at given times during your working set. You've got 3 major energy systems which are all unique in their own way and to maximize your body composition changes and performance levels it's very important that you train them specifically. The prescribed rest periods can help any training plan specifically target different energy systems at different times.
This means that you're able to improve overall body composition and maximize performance, so do NOT overlook the prescribed rest periods.