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It is by now well-known that wireless networks with file arrivals and departures are stable if one uses $\alpha$-fair congestion control and back-pressure based scheduling and routing. In this paper, we examine whether $\alpha$-fair congestion control is necessary for flow-level stability. We show that stability can be ensured even with very simple congestion control mechanisms, such as a fixed window size scheme which limits the maximum number of packets that are allowed into the ingress queue of a flow. A key ingredient of our result is the use of the difference between the logarithms of queue lengths as the link weights. This result is reminiscent of results in the context of CSMA algorithms, but for entirely different reasons. [ABSTRACT FROM AUTHOR]