I understand that its on purpose that the weed grows faster than its possible to cut it, though I can't say I really enjoyed it. I think this is one of those games where doing exactly the same, but flipped on its head - so slower growth, with the goal to cut them all, would be more engaging.
That being said, with Your concept I think it would be great if some form of level was involved. Like narrow spaces should gate the growth on one side - it should be the player's job to keep the slowly growing grass on one side.
I appreciate that there were those bursting tomatoes, though they made mostly hole, which quickly grew back. I think something different like flamethrower would be wicked for this game. It could even for short time flip the growth the other way - by spreading fire.