I'm not sure if I understand your question.

Why would a family not want that for their daughter?

For clarity, when the ottomans expanded into new territory would they want their daughters to marry a local noble? I think was the idea.

It depends on where in the empire you were. If you were in an ethnically charged area (such as Bulgaria) it would be seen as shameful for a young Bulgarian woman to be married to a Turk or to be in the Harem. This racism still exists today and older generations will frown upon such marriages.

Edit. Just read through the other replies. In general a Turk would rule as a regional governor, and the locals would not want to wed their daughters to Turks. I do not know about the other perspective.

I am Turkish and il be honest it would be considered shameful for an Ottoman young woman to marry like let's say a Greek noble that surrendered to the empire. On the other hand it is very common for foreign young girls to marry the Sultan or his noblemen. AKA Harems