EA 12.1 also describes jhānas, in the Contemplation of Principles section. Moreover, numerous other Chinese Agama parallel texts regarding Satipaṭṭhāna provide similar descriptions.
Theravada is multifaceted. Hau Xuan Tran wrote a detailed study comparing treatments of Satipaṭṭhāna given by Ajaan Lee Dhammadharo and Mahāsi Sayādaw:
Interesting. I’ll have to look into those.
All in all, I absolutely agree that many modern techniques are a product of the Burmese system, but I think it would be a stretch to attribute the contemplative aspects described in MN 10/DN 22 to any modern trend. No doubt, the suttas of SN 47 consider a broader range of applicability, but not so broad to discount that each of those four foundations of mindfulness play a direct role in the development of knowledge when the extent is available for discernment. I hesitate to say “insight” as to avoid the heavy connotations of the Burmese influence, but there are times for knowledge on account of samadhi, and of samadhi on account of knowledge. They go hand in hand, literally.
I totally agree with you, each of the four Satipaṭṭhānas contributes to the development of knowledge.