I have finally listened to the 2-hour talk by Stephen Batchelor (thank you, tiltbillings) on Buddha nature. Batchelor contrasts Buddha nature with Mara nature, saying that these are two sides of the same coin, and that it depends on our effort which one we develop. I think this understanding is helpful in as far as it prevents the most obvious misunderstanding, namely that Buddha nature is a given. Batchelor also mentioned that the English term 'Buddha nature' is a translation accident that occurred earlier last century when Chinese Mahayana sources were translated by people like D.T. Suzuki and others. The more correct translation would be 'Buddha womb'. The proper understanding of this very term would probably have prevented some of the above discussion.
The original term Tathāgatagarbha does not imply thingness, essence, or even atta/atman, which may be associated with the English term 'Buddha nature'.
My conclusion is that whether the teaching is helpful, depends on the practitioner's level of development and -perhaps most importantly- on his/her karmic disposition. Rowyourboat believes that the idea of suffering prompts people to progress rather than the idea of Buddha nature. -I think it depends.- If you experience relatively gross levels of suffering, then the overcoming of suffering (in the sense of the 4NT) is probably a very good motivator. But what if you experience positive karmic fruits, if you are materially well off, have loving family and friends, a well-paid job, etc., in other words - what if life runs smoothly, except for the occasional smaller annoyance?
In this situation, people might spent time with relatively refined pursuits, and the idea of Tathāgatagarbha can become a powerful motivator on the path. It is like a signpost that declares the ultimate goal. It reminds you that all you have achieved in life, such as relationships, career, wealth, etc. is impermanent. It is a challenge to go further. It is a challenge to go even beyond the initial spiritual achievements which may have secured calm and peace of mind. This is the sort of situation, where tathāgatagarbha becomes meaningful. So, it should probably be considered by people enjoying good karmic fruits and intermediate practitioners.