I believe dumping your trash in your neighbor's lawn is illegal. Burning unwanted agricultural crops apparently isn't. You could make burning the crops illegal too, which would also solve the problem, but that would probably face legislative barriers. Paying the farmers to do the right thing might be the most straight forward solution.

For basic household rubbish? Yeah, state should definitely pay for that since it's in everyone's interest. I'm not sure you'll find much opposition here.