They tried to take over a few times and the rebellions were crushed.
Remember Turkey rules the Arab world for over 400 years and as their empire crumbled, the Yeniseri moved to various areas of the Arab worl and intermarried with th local groups.

I will try to stay away from the term white slavery because it is a modern term that really does not fit the discussion.
The last dynasty came from Yugloslavia and entered Egypt as a way to give rebirth to dynastic inheritance but this didn't last long. WIll try to post something substantive over time.

2. During the reign of the Abbasid caliph they began to import more Turkish guards. This eventually lead to getting rid of Arab bedouins recruited for the armies. The largest portion of Mameluks came during the time of Salah-al-Din under the rulership of the Ayyubids.

3. The desendants of the Turks,Albanians,and Mamelukes still exist in modern Egypt. Many are part of the elite class in Egypt often called afrangi as opposed to baladi[indigenous]

4.White slaves were very common in Medieval Cairo. Most were eastern European Slavic women often valued as harem women. Basically they were sex toys for prominent Sultans. Most unions born of these harem women were freed;thus they lived a free lifestyle.