You can also buy some sort of fertilizer item when your store expands to the maximum size. I hear this speeds up the regrowth process a lot. The combination of the slow deterioration, fast regrowth and boost makes the animal tracks SIGNIFICANTLY less problematic.
Rumour has it that there will also be a day when you can get an item from the garden shop that's basically the equivalent of a lawnmower. With established paths, it's a lot easier to stick to the roads and not turn your entire town into a desert. That said, there haven't been any towns reported to have major desertification the way City Folk had. I've been keeping an eye open and it seems as though they really balanced it to the point where its harder to keep paths than it is to keep grass. Hence the lawnmower-effect item.