The problem with planting haphazardly is that you end up with an entanglement of vines like this

They run for several meters at a time with shoots going into the ground every so often. But these shoots break easily. So you end up pulling in the vine, breaking a bunch of the shoots, and leaving taters in the ground. Most of them are fingerlings but occasionally you get a huge one. And in any event, if you don't get all of them, they'll come back next year.