Yes, you have to remember a cross was used for what it was, an instant recognisable and simple to build indication of a grave on a battlefield, I would imagine the battlefield would have been littered with tons of wood from the destroyed trenches, some standing upright, therefore a simple and instantly recognisable sign of a fallen hero would have been required and the fastest and cheapest to construct and place would have been a simple cross, the Id tag of the person often being nailed to it.
That with the Poppy came to symbolise the war, hundreds of thousands of simple crosses marking the dead and the Poppy that flourished over those far off fields.