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Editing ConceptZoom entries worked for me too. I got rid of the left-trigger-problem and now have a perfectly working free-look on my xbox controller.
Here are the step by step instructions:
0. Set the key bindings in the game's key bindings menu as you whant them and save the settings.
1. Quit the game.
2. Open PROFSAVE_profile file in a text editor. The file is in Documents\Battlefield 4\settings folder.
3. Locate in the file this entry:
GstKeyBinding.heli.ConceptZoom.3.button
4. Change the numeric value after this entry to the same value that stands after
GstKeyBinding.heli.ConceptZoom.2.button
5. As described in Steps 3 and 4, change the value for entry
GstKeyBinding.jet.ConceptZoom.3.button
and then for
GstKeyBinding.vehicle.ConceptZoom.3.button
6. Save the PROFSAVE_profile file.
7. Enjoy!
NOTE1: You may need to remove all other GstKeyBinding.heli.ConceptZoom.# entries where # is the number 4 and higher.
NOTE2: You may need to switch from cockpit view to 3rd person view and back, for the free look to start working in jets and helis.
NOTE3: If on starting the game first time after the change, Origin reports that your local saves do not match the saves from the cloud, choose to use your local saves (not those from the cloud).
Thanks to all who helped in figuring this out!
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