Power users become powerful by accumulating tools
The best answer really is "Hollywood magic": the blow-by-blow work of software design does not look exciting to an observer, and so filmmakers look for heavily-visual metaphors that they hope capture the essence, if not the true form, of the activity. Sometimes they succeed in capturing the dimensions that matter to their story in a way that is honest if not literally true, like in Swordfish. Other times, they produce something patently absurd and comically stupid, also like in Swordfish. I think there is probably not just one best way to present software work in movies, because storytelling aims and context matter so much.
But that is not the only reason hackers and programmers in fiction seem to wield so much power so easily.
In the real world, people who work in software for many years collect tools that help them accomplish common tasks faster, better, and more easily. Programmers rely on re-use and automation to amplify their productivity.
Consider: the first time I try to guess someone's password, I probably have to write a program from scratch that can generate every possibility, and then write another program that can take an individual guess and actually try it out, and then I have to wire them together.
The second time I try to guess someone's password, I can probably re-use the first program, and I might be able to re-use the second program if their account is in the same system as the first account.
The 50th time I want to crack someone's password, I run my CollectTargetPersonalInfo program, which scrapes Google & Facebook & LinkedIn & Instagram & Twitter to try to collect any public info about the target -- full name, birth date, immediate family names, etc -- which then generates a "target profile" that my PasswordGuesser program uses to prioritize different regions of the keyspace.
The 700th time I want to crack someone's password, I just send an email with their name to my PasswordCrackerBot, which runs in the cloud. It adds the name to a list of people it is researching and attempting to crack. When it finally succeeds or gets locked-out, it replies to my email with the results.