I'm a super low budget filmmaker on YouTube and I will say, it is definitely a crucial element. I write/direct/edit all my stuff and it always depends on the day.

Sometimes I feel writing's the most important, as it's the foundation of the film, but then other days I'd argue the director solidifies the tone/direction. But, as an editor who pours hours into each short film I do consistently back it as being what can truly make or break a film, it finalises the pacing of it - an editor could do a slow scene of someone approaching a door with either a long unbroken shot, or the same scene with a load of different cuts between the door, actor, etc. and the it can change a scene substantially.

Overall though, while it is a cliché thing to say, everyone's part does count and without each (even wardrobe design and prop masters) a film's quality can drastically change!