Synthetically generated speech has rapidly approached human levels of naturalness. However, the paradox remains that ASR systems, when trained on TTS output that is judged as natural by humans, continue to perform badly on real speech. In this work, we explore whether this phenomenon is due to the oversmoothing behaviour of models commonly used in TTS, with a particular focus on the behaviour of TTS-for-ASR as the amount of TTS training data is scaled up. We systematically compare Denoising Diffusion Probabilistic Models (DDPM) to Mean Squared Error (MSE) based models for TTS, when used for ASR model training. We test the scalability of the two approaches, varying both the number hours, and the number of different speakers. We find that for a given model size, DDPM can make better use of more data, and a more diverse set of speakers, than MSE models. We achieve the best reported ratio between real and synthetic speech WER to date (1.46), but also find that a large gap remains.