On one hand, you'd be going against the established guys - Moto Mader and Moto Center Thun/Bern - but these guys are at the high end, price wise.
I think that an Africa Twin would be a great bike. I always rented 1150/1200 GSes when I was renting and now have one of my old bikes over there, but neither of the above were really well suited to exploring some of the smaller roads. The rentals were expensive if you scratched them, and my old Suzuki is really only happy on paved roads.
Your biggest hurdle may be from the insurance standpoint, but it sounds like a good idea. Keep in mind that you will probably need to do more maintenance on the rental bike than you would if it were just yours. I wouldn't want to rent a bike for a week or two and worry about worn tires or chain, for example. Just an item for thought.