I've seen previous series of Masterchef The Professionals, and generally the skills test is in order to test that the cooks can show good industry standards and cooking practices.
In one that I saw, they were asked to roll out dough into several shapes ready for cooking. They were then graded on this, without any cooking involved at all. One of the contestants was praised for forming two balls of dough into the shape for bread rolls simultaneously using both hands.
Obviously when it comes to cooking forming them separately would be fine, but in a busy kitchen being more efficient and performing the tasks quicker would be beneficial, which is what they were looking for the contestants to do from their own skills and knowledge of professional cooking.
Therefore cooking the onions and then cooling them on a freezing tray would be a technique used in professional kitchens, in order to cool the onions as quickly as possible so that the burgers could be formed into shapes before cooking, and the chef could move onto other prep work before the service begins.
As @moscafj points out, the onions would need to be cooled for safety reasons, as the burgers would likely be formed prior to service and then left to be cooked to order later in the day, therefore the onions would need to be cool before being combined with the raw meat to ensure it does not begin cooking prematurely.
As for it falling apart, I haven't tested but perhaps allowing the beef to warm from the cooked onions, then cooling down before the service begins and finally cooking would cause the structural integrity of the burger to be inconsistent, which is something required in professional kitchens.