The term "Advertising" is just a small part of a businesses Marketing mix. All the things you mentioned also form a part of that mix.
Jims is a huge brand, regardless of any franchise negativity. His big boof head can be seen on anything from the side of a van to the side of a pen.
The key is to have your Market think "geejay" or what ever your business name is, instead of Jims when a customer thinks "Lawn Mowing". If you stop advertising or "your brand" goes underground until you "need" work, then the Franchise wins because they are ALWAYS in everyones face.