16th century Albania native Lütfi Pasha, who had been conscripted/enslaved himself in the devşirme levy on Christian boys for the Ottoman military and administration, thought it was a super awesome deal. And why not? He'd leveraged the system to rise from an economically disadvantaged dhimmi family in the backwater Balkans to become Ottoman grand vizier.
And the thing was--that was no accident. The purpose of devşirme was to produce the ultimate loyal soldiers: men who owed absolutely everything they were to the Ottomans. So when Lütfi Pasha, a man with a great deal of investment in the success and stability of the Ottoman Empire, argued that devşirme needed not just to continue but to remain the primary or even exclusive engine of social mobility, he had in mind the general outcome of the system as a whole, not just his own remarkable story.
As Linda Darling and others have pointed out, in the late Middle Ages, being an "Ottoman" was a matter of what you did rather than who you were. As the core Turkish tribes became a polity, an empire, fighting in the Ottoman military basically qualified someone as an Ottoman. This core trait/experience lodged in both Ottoman imagination and law as the empire entrenched itself in the early modern era. Military service was the major pathway to the social status that brought with it money and power.
The 15th-16th century Ottomans instituted a form of land tenency/oversight/usufruct, the timar system. The government handed out as rewards or payment a land grant known as a timar. This gave the recipient not precisely ownership over the land, but the ability to live there, the responsibility to oversee it, and most importantly, a good chunk of its tax revenue. You'd not be wrong to draw comparisons to the layers of lords in medieval and early modern Europe--in fact, there were levels of timar, too, with the more powerful men essentially (or actually) becoming regional governors.
In general, military service was the way to earn a timar. (And during the few periods when other pathways opened up, as there was not enough warfare to produce timar-winners in that method, you better believe successful soldiers complained bitterly about those other pathways not being good enough). The key to the importance of the devşirme system and the desire of dedicated Ottomans like Lütfi Pasha to preserve it was, military service was a very limited opportunity.
There were, in theory, two paths to military service. The infantry was primarily a slave force--but since Muslims cannot enslave Muslims, that limited the ranks to Christian men taken in the devşirme (and forcibly converted to Islam afterwards), and purchased or captured slaves. The cavalry might include some transfers from the Janissaries/infantry, but was primarily composed of the Ottoman hereditary quasi-nobility, the sipahis.
The goal of this limitation was severalfold. I mentioned that ensuring the loyalty of troops and advisors was paramount. You might contrast this with the situation of Albanian warrior-noble Skanderbeg, a Christian sent to the Ottoman court as a hostage who spent quite a few years ripping it up in Turkish military service--only to turn shoulder and became an Albanian hero leading the fight against them.
But another important reason was to limit access to the social and economic mobility available to successful fighters. Lütfi Pasha pointed out that the Ottomans needed peasant farmers above all, so it was not good for boys to leave their farms at whim to attempt to join the military. A more cynical perspective points out that limitations like the devşirme allowed the Ottoman government to very carefully control the number of people who might have a chance at competing with them for timars and the wealth/power they afforded.
Obviously, these sharp restrictions were normative. And it's precisely because they were sometimes violated that Lütfi Pasha, even in retirement, wrote so vehemently in favor of preserving the sipahi/devşirme limitation on military service. But underneath that, what we see in the writing of someone with a very big stake in preserving the stability and success of the Empire, is a belief that the devşirme system worked to produce loyal soldiers. That is--men born and initially raised Christian who were conscripted/enslaved but came to see it as benefiting them in at least some part.
Future soldiers, advisers, and even grand viziers weren't the only people affected by devşirme, of course. The evidence from the Balkan "home front" is...somewhat mixed, in a very bittersweet sense. From the standpoint of Christian communities as a whole, devşirme was very understandably something to be avoided if at all possible. When merchant colony Galata, right outside Constantinople, fell to the Ottomans on their way to the prize, the Italians (Christian) were very keen to negotiate an exception to the devşirme for their town. And in fact, they did!
On the other hand, it seems to have been the case that some (I stress some) peasant families wanted their sons to be taken in the devşirme. Conscription/enslavement wasn't universal, of course, and the Ottomans were careful to choose those boys they thought would make the best soldiers (strength, health, brains). Well, there are records of Ottomans being bribed to take boys they might otherwise not have. Since this is a pattern that only shows up gradually, scholars have generally argued it was because news of just what devşirme conscription could do for the slave had filtered back. Poor families wanted good things for their sons. There's been a lot of work recently on the Christian-Muslim "divide" and conversion or performed conversion across religious boundaries, including/especially for reasons of social benefit and safety. Although most of my own reading here concentrates on women converts (in both directions), this still suggests it was absolutely not out of the question for Christian parents to see the departure of their sons with devşirme as a horrendously mixed blessing/loss: to send away a son forever on the promise he might live a better life.