We propose a novel approach for blind room impulse response (RIR) estimation systems in the context of a downstream application scenario, far-field automatic speech recognition (ASR). We first draw the connection between improved RIR estimation and improved ASR performance, as a means of evaluating neural RIR estimators. We then propose a generative adversarial network (GAN) based architecture that encodes RIR features from reverberant speech and constructs an RIR from the encoded features, and uses a novel energy decay relief loss to optimize for capturing energy-based properties of the input reverberant speech. We show that our model outperforms the state-of-the-art baselines on acoustic benchmarks (by 17% on the energy decay relief and 22% on an early-reflection energy metric), as well as in an ASR evaluation task (by 6.9% in word error rate).