Fear of robbery might motivate a locked cash drawer, or no cash accepted at all. But only one person in the store being able to operate the cash drawer? The most generous explanation for this I can think of is the business fears their own employees are thieves, and want to reduce risk by only trusting a small number of them to handle cash.
But this doesn't explain why it's so hard for even the employee with the cash drawer credentials to open the drawer in a timely manner. They go full hackerman on the keyboard, scratching their head and cussing at the computer with utterances about the value of technology that would make the unabomber proud. It seems obvious to me the workflow for opening the cash drawer is inexcusably broken.