Slave uprising are rarely successful, and are usually very brutal. When successful, most of the time, most non-slaves are murdered, and many times, many of the slaves are not freed. More likely, there is huge amounts of blood shed among the slaves, followed by worse slavery.
Let's use the Holocaust as an example. There were few escapes from the Concentration Camps, so under your theory, they rose up and the Holocaust was quickly ended from within. Except they did not. Not only that, but few on the outside knew how bad it was, so there was no a rush to end the Holocaust. More escapes would have meant more on the outside knew how bad things were.