Why do you need two voltage sources in a switched capacitor realisation of a continuous resitance?
Would the circuit not be the same with a single battery of V2-V1?


Yes it would but, that is missing the point of what the diagram is telling you. If you had a single battery then, that means that the equivalent resistor formed by the switched capacitor is ground referenced so, and ask yourself, how important that configuration is compared to showing a more generalized circuit that can be ground referenced but, can also be used as a series element.