I can see some benefits for the slave soldier system: Namely, these soldiers tended to be very well trained, organised, disciplined, and armed, and as a result were very effective. The Mamluk sultanate is a great example, they managed to fend off the Mongols while eventually completely expelling the crusaders from the middle east. The Delhi Sultanate used it's Mamluk soldiers and generals to repeatedly beat back the Mongol invasions of India . The Abbasid's had very effective Turkish Mamluk's who were good generals. And finally, the Ottomans had the ever famous Janissaries, technically slave soldiers who were noted for their exceptional skill in battle.
However, I see a lot of negatives of the slave soldier system as well: These slave soldiers tended to form their own caste over time, and as a result could exert serious political power over the affairs of the state, and even the ruler of the state himself. Think the Janissaries in the 17th century, who deposed various Sultans and even killed one, Osman III. Or the Abbasid Turkish Mamluks, who also deposed various Abbasid Caliphs. Even the Mamluks became a state because they executed the last Ayyubid sultan and took power for themselves. Hell, you could even make comparisons between these Muslim slave soldiers and the Praetorian guard. These slave soldiers almost always tended to be very resistant to reform, because they were worried that reform threatened them. Take, for example, the Mamluks. I read that one of the reasons the Mamluk sultanate was conquered by the Ottomans was because they were fighting traditional style warfare while the Ottomans had adapted to more modern forms of warfare. The Ottomans themselves had a problem with the Janissaries when they were trying to reform the military as well, with the Janissaries either revolting or deposing the Sultan. These slave soldiers also tended to be a tiny amount of soldiers, making it very difficult for them to use any numbers against their foe. The Mamluks, using them for another example, were almost always outnumbered when fighting the Mongols and later the Mamluks
So, why did various Muslim polities use slave soldiers? why made these slave soldiers so desirable? and why did the slave soldier system almost always end up going bad in the end?
I've seen two different explanations for this phenomenon, which are not necessarily mutually exclusive. In The Origins of Political Order, Francis Fukuyama argued that the Arabs first started recruiting slave soldiers to create a counterbalance against powerful tribal factions within the umma- as ethnic and cultural outsiders who happened to also be the sultan's personal property, they weren't entangled in Arab clan politics. In Empires of the Silk Road, Christopher Beckwith argued that the institution was derived from the Central Asian practice of leaders maintaining a comitatus of sworn followers, and its adoption reflected the degree of Persianization/Sogdianization of the Islamic world from the Abbasids on. But there's no reason why both can't be true- that the Arabs first got the idea from Central Asian subjects, then adopted it widely because it was useful to them.
Why would these groups become problematic? For the same reasons any other military or political caste would- maybe their privileges become too well-established and they become a drain on state resources, as the janitschars did. Maybe they become so effective at running the state that they decide they don't need the sultan anymore, as the Egyptian mamluks did.
To add onto this question. What is the difference between a slave army and pressing civilians into military service?