I've always been a big fan of dirt paths in the game, but they get taken over so quickly by grass and forest terrain. Don't get me wrong, I love that mechanic.
I would however like to see some way to create persistent dirt paths. These could 'decay' outside of claimed land, just as tiles do.
Here are several options that I see:
Salt the Earth
Spread salt on a tile to prevent it from growing any grass or forest tile.
Can be reverted by plowing, or planting grass seed.
Would require new recipe to 'break' salt down into more uses, so it wouldn't require a ridiculous amount to create a short path.
Gravel path
This is slightly different than the way 'stomp to dirt' looks, maybe a bit of rocks thrown in, some grass around the edges.
Crush 'x' amount of any rocks into 'gravel' item.
It would function just like pavement in terms of decay.
Desire Paths
This would be the coolest option probably, but also the hardest to implement.
The terrain would register where it's walked on commonly, and turn to dirt if it's stepped on 'x' amount of times.
The tile would then also be more resistant to natural competition by grass and forest tiles moving in, this would create an even more natural feel.
As a disclaimer, I know you can effectively create 'dirt' paths by outlining them with pavement, but it just doesn't work as well for a natural aesthetic.