For much of the early history of the Ottoman Empire, the succession mechanism was fratricide; when a sultan died, there was a civil war among his sons and their supporters, with the winner ending up as the next sultan, the losers dead, imprisoned, or in exile. On the face of it that is an expensive way of choosing a ruler. On the other hand … .
The early sultans commanded in battle, presided over the meetings of the council of state that made policy, played an active role in the running and expansion of the empire. Eventually they abandoned fratricide. Also eventually, the role of the Sultan shifted. The council of state was run by the Grand Vizier, who merely reported to and consulted with the Sultan. The armies were commanded by generals. The Sultan withdrew into luxurious isolation.
The obvious conjecture is that the two changes were linked. Fratricide was expensive--but it selected the claimant best able to win. The result was to put at the head of the empire able, aggressive, politically and militarily competent rulers. Abandon fratricide and eventually the ruler becomes a figurehead.
During the early centuries, when the Ottoman Empire was not engaged in a large war it was engaged in small ones--regular raids across the border to bring back loot. Such raids depopulated, and so weakened, the border territories of nations adjacent to the Empire, making conquest easier. And they gave people living in those regions at least some incentive to want to be conquered, in order to get to the side of the border raids were coming from instead of the side they were going to.
Raiders received tax advantages from the Empire, but were largely motivated by the desire for loot. Poor peasants do not have much worth stealing. But in a slave society, the peasants themselves are worth stealing. Thus the institution of slavery, by helping to make possible a cheap form of military force with which the Ottomans could harass their neighbors, gave a real advantage to an expansionary state.