I saw a documentary that claimed that the Ottoman had ten very competent sultans back-to-back during its period of expansion, and that this could be partially explained by the necessity of eliminating all competition (brothers) in order to become sultan. Is this a reasonable claim? Are there other explanations?
The short answer to your question is: The reason the Ottoman State internalized fratricidal succession practices is that they couldn't trust outside rulers to hold on to hostages. Before the practice was started, many Ottoman rulers sent their siblings to be held as political "hostages" (having a different meaning in this case that currently, here it means more of a dignitary or pampered guest) to different polities around the Mediterranean, namely the Byzantines in Constantinople. Problem was, whenever the Byzantines didn't like what the Ottomans were doing, they would release the hostages and start a civil war within the Ottoman Empire. To solve the problem, they just killed all their male "issues". If you want an incredibly interesting story about how the loser could escape and then be a problem requiring the espionage of an Ottoman Spy, look up "Cem Sultan", it's quite a story!
Source: Caroline Finkel is my go to gal on anything Ottoman. "Osman's Dream" is full of great info on Ottoman traditions. Check it out!