Small Potatoes: Obtaining Tubors Without Villagers' Help

I think that potatoes, carrots, and beetroot should be obtainable without getting them from villages and chests or killing zombies.  My idea is a "cultivation system" similar to wheat, but a little different.  I will use potatoes as a demo, but these techniques will apply to all root veggies.

To get wheat, you must first cultivate it from its "wild" state, tallgrass.  In a similar manner, while wandering through the plains, you'll find some odd-looking weeds interspersed between the flowers and grass.  These plants are wild potato weeds, and you can break them to get around 1 small potato.  Small potatoes are pointless as a food source, being uncookable and restoring only half a hunger.  However, they can be planted in farmland, to grow more wild stringy potatoes.

Being grown in nutrient-rich soil (farmland), these potato weeds have a small chance of dropping a regular-sized potato when you harvest them.  Once you have a regular-sized potato, your cultivation expedition is over!  Plant this regular-sized potato in some farmland to get the tasty potato you find in villages.  As said before, the same strategy works for farming carrots and beetroot.

I like this idea since it's simple, and makes the game more interactive.  It also means that players about a day or two into the game can already have access to these delicious tubors, allowing beginner players to add some spice to their plain ole' wheat farm, as well as being able to farm pigs.