The field content is a field item list and normally you would need to include a single value also in an array. The fact that you can set a scalar like in your example is due to extra code in the Field API detecting the scalar and transferring it to a field item list with a single value. To delete the field you can’t set an empty scalar, though, because this would be interpreted as a single field item with that empty value.
So to delete the entire field content set an empty array:
BTW you can get the entire field content:
$values = $node->get('field_nom')->getValue();
Change the array $values and set it again: