I think yes and no are both right re. labour!
Thing is, over there a lot of livestock was kept inside for the winter, as it could get very wet and mucky.
So....if straw had to be carried to them, battens would be easier than trying to carry chopped stuff. But Yes,the work of forking all the bundles up onto the threshing deck would indeed be more work, plus stacking the battens into a straw stack would be more work.
It's very much a case of systems adopted according to needs I suppose.
Attached are a couple more pics, showing a straw stack being built for winter use.
All these pics are about 1910.