I can't speak for the official reasoning, but the internal motivations were understandable enough:

The Sultans wanted to prevent horrific succession crises that literally ripped the Empire apart. On succession, interest groups would claim successors and use them as lightning rods to push their own interests; this occurred frequently with the Anatolian Turkish nobles who had been forcibly incorporated into the Empire and wanted greater autonomy for themselves. It also didn't help that the way how succession worked for awhile was that the son who took power would usually be the one who makes it to the capital first. This is why Sultans would place preferred successor as close to the capital as possible, and plotters would situate their preferred successors closer as well.

As strange as practiced fratricide may seem in our eyes, it was intended keep things relatively stable and peaceful internally for The Ottoman Empire.

Source: Osman's Dream: The History of The Ottoman Empire. Caroline Finkel.

To add to /u/Yarhammer's answer, succession crises in the medieval Middle East were far from unheard of, and you would often find family members given positions of power in other locations could cause trouble.

This especially came to a head, however, during the so-called Ottoman Interregnum at the beginning of the 15th century, where the sons of the Sultan Bayezid all vied for power following their father's defeat by Timur. The chaos which ensued could have ended the Ottoman polity. There is a very good book on the topic of the Interregnum written by Dimitris Kastritsis, who has been working on this period since his Ph.D., entitled The Sons of Bayezid: Empire Building and Representation in the Ottoman civil War of 1402-13.