From what I understand, Tendai monks such as Dogen, Nichiren and Honen left Tendai and embarked on "single practice" schools (Zen, Nichiren and Pureland respectively), due to their thought that this one practice was better/easier to attain enlightenment. From my little understanding, Nichiren believed that his school was the only correct way to enlightenment, whereas Dogen and Honen wanted "better/easier" ways to enlightenment.
I don't know much about Dogen, Nichiren or Honen or the later development of their schools. Certainly Tendai was the cradle for many eminent Buddhist practitioners in Japan because it was so well established and influential there. But I think it a simplification to say in every case that these guys struck out on their own as a rejection of Tendai.
For example, Eisai is often pointed to as the first to establish Rinzai Zen in a viable manner in Japan. He, however, never abandoned Tendai practices, and as far as I know still considered himself a Tendai monk to the end of his life. I have always preferred to think that the Tendai approach is what allowed
someone like Eisai to think it worthwhile to seek out and transmit Zen teachings/lineages from China...even if the official position of the Tendai hierarchy at that time was to actively discourage their establishment (for reasons that likely had more to do with non-religious concerns).
In any case, my personal opinion is that any teaching that reifies an interpretation of "Ekayana" which justifies inter-sect triumphalism is deluded. Any of us is a follower of the One Vehicle when we turn the light around and give testament to the essential point of all Buddhist teaching. Whether someone does this through nembutsu, deity practices, mantra recitation, koan, kaihogyo or whatever is really not the point. Or, so I've been taught in Zen.
...Tendai is a "big tent" culture.
That's what I like, and I'd love to see more exchange/encounter between different traditions as well (which is why I lurk around here). Our One Vehicle tent is certainly big enough for it
Sorry to interrupt once again.