There's no option for this at the moment. You will have to modify php code to hide this.
In each file displaying lines, you have a call like this :
$object->printObjectLines($action, $mysoc, $soc, $lineid, 1);
The last parameter "1" is here to says "display date selector".
This mean's you have to modify several files.
Better way is to change this in only 2 files ; core/tpl/objectline_create and objectline_edit.
Simply replace "if (empty($dateSelector)) $dateSelector=0;" at the top of the file by "$dateSelector=0;"
I'll see to make it an option.