"In keeping with its violent past, the last vestiges of Donatism vanished in the seventh century as its adherents were mowed down by the sword of Islam, the cry of "Deo laudes" being replaced by "Alahu Akbar," which heralded the Muslim subjugation of North Africa."
It has been argued that the weakening of the Church in North Africa by the Donatist heresy over the centuries made the work of the Mohammadens much easier, not merely in the killing but also in the converting. As we know, west of Eygpt, The Church essentially ceased to exist. It is a particularly dangerous heresy even today.
Everything you say is essentially correct and yet...there are still millions of Christians surviving in the Muslim dar - albeit tenuously - and even though Christians represent the longest and most persecuted group of religious people in history.
I suppose Muslims needed dhimmis alive to do their work: education, governance, labor, breeding, whipping posts, etc.
http://i-cias.com/e.o/christia.htm