Shaggy, i like your way of thinking. I like to use extreme cases to validate hipotheses.
In the infinite runway case, you still have limits: tyre speed, for instance. Not maximum brake energy speed, because all you would have to do is retard the throttles and smoke a cigar while you slows down.
In not so big airplanes such as B737, A320, etc... optimum V1 is just the same as VR, meaning that you have more runway than you need to stop the airplane (basically you have "infinite runway length" in case of stop). In these airplanes you will hear something like "V1, Rotate" in most of the take offs.
In the big birds, however, you will hear something like "V1", ".......", then "Rotate".
It is in the big birds where V1 is truly meaningful. At the V1 call they remove the hands from the levers. From then on they are going to fly whatever happens.
V1 also means that the airplane will be able to lift off, maintain v2 and then reach 35 ft by the end of the take off distance available. At V1 you can either stop or go safely. Depending on the circumstances, most of the times you can choose a V1 within a speed band. The trick is choosing the optimum one (the one giving max take off weight or max assumed temperature).
Then you have the climb and obstacle clearance consideration, which can have effects in the determination of the optimum V1, too.