Yea, that’s not right, at least not in modern film. The distance to the subject and thus the resulting focal length needed to get proper framing drastically impacts the look. Every (or at least most of them) Cinematographer and Director has their own preferences.
For example, Emmanuel Lubezki, the Director of Photography for films like The Revenant, Children of Men and Birdman prefers the use of very short lenses thus he has to get close to the subject while Ridley Scott as Director prefers the use of longer lenses in his films, moving the camera further away.
And all that has nothing in the slightest to do with focus or zoom. The opposite, motion picture cameras usually do not use zoom lenses but fixed focal (prime) lenses and tape, too was rarely ever used in motion picture production. Today they usually use various types of flash media (like SSDs or CFast cards) or, if they feel fancy, still analogue film.
In TV (live) production, that’s a little different. Tape or other magnetic storage media were used for a long time up into the HD era. Nowadays, SSD or SD recording is used just as well. Also, TV cameras are indeed usually outfitted with powerful zoom lenses since the convenience of fast zoom tops the image quality of prime lenses, especially in live settings. (You can’t just swap lenses when every second counts). But even then, going as far away as possible isn’t usually what’s done. It always depends on the circumstances, the location and the needs of the shoot.
Modern TV and motion picture cameras are large for a number of other reasons. They support a whole lot more features than a good video capable mirrorless photo camera (like a Sony A7 IV) like multiple video outputs in industry standards (SDI, not HDMI), larger batteries, hotswappable redundant storage, mounting points for additional equipment, microphone ports, support for more video codecs and higher data rates, higher resolution, etc. And of course, a whole bunch of cooling for prolonged use without any hitches or glitches.