Well, I have an opinion with no real supporting proof of why the Mahayana split: The doctrinal split was a justification of what had already taken place practically in earlier times. Here is my perspective.
We know that the Buddha and community was not only a spiritual movement--it was a social movement as well. The Sanga accepted people from all walks of life within the Indian social strata--Brahman, Kshatriya, Vaishya, and Sudra. While it is unclear, I suspect that there was an aspect of the emerging Buddhist movement--even during the Buddha's time--centering around the outreach to and upliftment of the disadvantaged and suffering within Indian society. Also, a number of the Buddha's disciples were from the warrior/administrative class (Ksyatriyas). This mindset emphasizes working for the welfare of the kingdom. There was a socially conscious aspect to the movement. My opinion is that these inclinations of members of the Sanga and laity resulted in a split of emphasis between those who were socially directed and those who were contemplatively directed.
There is such a split within both the Hindu and Christian traditions. Within the Hindu system, spiritual paths are split between Karma, Bhakti, Jhana, and Raja. I don't know the origin of this division but it acknowledges that some people prefer the path of action (helping others), some devotion, some wisdom and some integrated. Within the Christian tradition, there is a famous story of Mary and Martha. (You can look up the story if you are interested.) Mary represents the life of the contemplative/devotional approach and Martha represents the active/service (helping others) approach.
What this is pointing to is that every faith seems to have both a path of service and a path of contemplation. Not to say that they are mutually exclusive. Still, it seems to me that the Mahayana vow to help/save all sentient beings is a doctrinal elaboration of what was likely an inherent service-oriented inclination of a segment of the Sanga.
Again, this is just a theory...