If you get rid of lobbyists, you'd need to forbid citizens from writing letters to their politicians as well.
Little susie writes "Please sir, the chemical waste being dumped in my backyard has given me cancer, please revise the statutes so that hazardous dumping is not allowed in residential neighborhoods", and the letter is destroyed because it is a form of lobbying.
Careful when you wield that sword, it's big, and you might cut more than you wish.