A very short summary of the Vipassanā technique taught by S.N. Goenka would be: "observe your bodily sensations with equanimity". The role of physical bodily sensations is the key aspect of the technique and other traditions do not attach such a great importance to them. It is said that Goenka's technique of scanning the body to feel increasingly subtle sensations was passed on though several lay teachers and that it goes back to the Burmese monk Ledi Sayadaw.
Ledi Sayadaw left a large quantity of writings; some of them are available here and/or here. I looked through some of them, and in no place did I see any passage that would present observing bodily sensations as the technique to be followed. If he really taught this, it is hard to imagine he would not mention that this is the key aspect of the technique. Can anyone provide a relevant quote from Ledi Sayadaw's texts?
Update: The question is whether Ledi-style Vipassanā should be practised by observing bodily sensations/body scanning. Mindfulness of the body in Ānāpāna Dīpanī is presented as something distinct from Vipassanā, so it doesn't answer my question. Moreover, it looks like Ledi Sayadaw understood "mindfulness of the body" to mean "mindfulness of the breath", not body scanning. See Ānāpāna Dīpanī, part XIV:
[...] establishing mindfulness of the body (kāyānupassana satipaṭṭhāna). The out-breath and in-breath, being part of the aggregate of materiality (rūpakkhandha) are called body (kāya).