Every industry has specific names for specific jobs because those names have specific descriptions of what is or isn't their job.

A film set run's the most efficiently within a hierarchy for a reason and that reason is lot of specializations that have to work together towards a common goal. By your over-generalization about 10 different positions with very specializaed roles could be classified as handy man.

Would you call somebody that works in construction pretentious because their jobs aren't all "handy man" but are instead carpenter, plumber, electrician, bricklayer, welder.

A Key Grip first runs a team, he has a Best Boy Grip as his second in command, and the rest of the team are just Grips. The Best Boy has specific roles like handling filling out paperwork, timesheets, hiring etc., that the regular grips don't do.

Gripping is in large part a physical labour job, but it's also practical engineering, its shaping light, it's building contraptions and rigs and structures.

If that was the only job that has similarities to "handy man", you could have a point but there are at least 4 or 5 other jobs, and at least two other departments that have a "handy man" aspect to it. (The Art Department would arguably a lot more handy man as they have Set Carpenters, Art Directors, Productions Designers etc. All who work with regular tools.)

So call it whatever you want, but there's practical reasons for having specialized roles that have their own names, and it's no different then any other industry that has any sort of specialization.