I'll try to answer your question, sorry if it doesn't satisfy you. Firstly, it should be understood how some developments made the system came to be in the era of Murad I. As Ottoman territory become larger, the conquering lords fighting under the Ottoman banner acquired lands and revenues in the new territories, which established them as local powers, with their own troops and retainers like the Evrenos, Mihail, and Malkoch families. At the same time, the Ottoman conquerors frequently did not remove the dynasties that had ruled in pre-Ottoman times, but instead maintained them as vassals under Ottoman suzerainty. On the other hand, Murad was the first sultan to execute his brothers, with the result that the Ottoman realms were no longer the shared patrimony of all members of the ruling family. Sultans’ sons continued to act as provincial governors and army commanders, but strictly under the tutelage of their fathers, and without the freedom of action that their predecessors enjoyed who could become a semi-independent military commander and governor.

These appearance of the marcher lords, and the continued rule of semi-independent local dynasties clearly limited Murad's power. He was not an absolute ruler, but rather the most powerful in a confederation of great lords, who were his allies and vassals rather than his servants. To establish their own position, Murad and his successors had to secure loyal men who were subordinates rather than confederates, and whose loyalty to the Ottoman dynasty was unquestionable. With the absence of modern institution, one way to obtain such men is from the sultan’s household, where its members can be employed as governors or soldiers.

Now, the institution of slavery and the employment of "foreigners" is the easiest way to form such household. Islamic law permits slavery and creating a category of 'licensed slaves' makes it possible for them to carry out transactions on their owners’ behalf. Slaves could therefore become trusted and important figures. Furthermore, despite their status, through membership of an elite household they could occupy a high social rank. The 'slave household' had become a feature of Islamic Societies from the Abbasids who employed slaves as soldiers and government officials, to the Seljuks who employed slaves as troops and military commanders, in the palace and in the government, and had even established a school in Konya for their education. With those precedents, including the elimination of the sultan’s adult blood relations from the household and government, it seems inevitable that the sultan must form such 'slave household'. Recruitment into the imperial service therefore usually meant recruitment as a slave.

In the Islamic law, Muslims and Non-Muslims who were living in Islamic lands cannot be enslaved, so to form such household, the sultan instituted the Pençik system, where the sultan could levy the captives brought by raiders to be recruited as soldiers or officials. The first members of the Janissaries were also Pençik levies. However, after some time, it was clear that supply of slaves from outside the Empire’s borders was insufficient to fulfill the demands for household members, and there were downsides from the captive levies too. Those captives were mostly already mature men who were not very responsive to Ottoman military training like the training for Composite Bows, main weapon of the Ottoman army which was very demanding and time consuming. In addition to training, loyalty was also an issue. Most of those captives, who already had undergone hard training and who lived in prison-like conditions were obviously unwilling to work for a foreign power, so a substantial percentage of them were ready to desert the army in any suitable opportunity. Field commanders had to take special measures like establishing special police units to keep the deserters in check.

Thus, to counter those deficiencies, the Ottoman Sultan then established devşirme, the system that you just described. The devşirme has advantages that covers the deficiencies of the Pençik system. First, There is a large and reliable pool of men available for selection, Second, children were more responsive to the training, and their bodies and minds were easily molded according to the needs of the military, and Third, in the long and complex training, heavy emphasis was placed on unit cohesion and solidarity, and very rich rewards were granted for merit and combat achievement, which combined to create intense loyalty to the institution. In fact, loyalty to the sultan never became an important issue, as in reality blind obedience to the orders of the superiors was the generally expected norm. Of course, this caused a legal issue up to the sixteenth century because it contradicts the Islamic law of not enslaving Non-Muslims in Islamic lands, but such issues were mostly ignored and the practice is continued up to the eighteenth century.

Sources:

"A Military History of The Ottomans" by Mesut Uyar

"The Ottoman Empire, 1300–1650" by Colin Imber