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Rudags - it depends on the philosophy of the gym, the equipment availible in the facility, the training of the coach, the level and years experience of the gymnast and since you are asking about gymnastics the event they are coaching as to whether they spot or not. Gymnastics uses so many more drills before skills, body position drills to create muscle memory, repetitions of parts of a skill before attempting the entire skills, and conditioning that is both general and specific to the skill the gymnast is working on. Compulsory routines demand a certain set of skill progressions along with a set score before the athlete can be promoted to the next level. All of this lessens the need for spotting as much on most of the skills that we use in cheerleading.
The trampoline to tumble track to rod floor or pit to floor transition is commonly done without spot. Again the type of equipment and knowing how to use it greatly lessens the need for a spot. The primary purpose is for the gymnast to learn spatial awareness and know what they are doing in the air. They learn how to open their eyes and see (also called spot) certain things instead of just feeling it or throwing it. The fear of falling is usually minmized due to early training. First thing a gymnast learns how to do is fall. The secondary purpose is to build confidence in doing the skill by themselves.