The answer lies in the methodology of how Sharia is compiled and interpreted. Islamic law is extremely path dependent, so that theoretical inferences are drawn from what is clearly referenced from the Prophet's life and applied to new situations, which leads to new institutions, like. slave-soldier recruitment. Inferences drawn from these are applied to newer situations and so on.

This is how it went: The earliest Holy Wars were fought by people organized as clearly segmented tribes under the leadership of their chiefs. Alongside them fought believing slaves from places such as Ethiopia and Persia. There was a requirement for every able believer to fight. This much is recorded in the Sunnah.

Now, from this it can be inferred that there are 3 legitimate ways of recruitment: slaves brought along by their masters, allied tribes recruited as a whole and those who are bound as Muslims to a religious duty.

Apply this to the practical situation existing in the 9th century and you get the answer. Out of these 3 options, tribes were difficult to manage and you didn't want to empower the common folk Fellahin too much. So slave-soldiers directly owned by the Sultan became most convenient.

Yes, there are sects. The Shia-Sunni split is the result of a fracture among the very earliest companions right after his death. But within the Sunnis (who are and always were the vast majority) doctrine is pretty much the same. Only minute details of ritual vary, not enough to profoundly affect political structure. Even Iran wasn't Shia majority until very late and Egypt remained Sunni through decades of Shia rule.