You are right the fact that freeing slaves was instituted as (Kaffarah) didn’t really help to reduce the magnitude of slavery practice. On the contrary Slavery Trading had flourished as a result of conquering other nations.
Unfortunately some Arab countries kept the slavery practice until the 20th century. In Saudi Arabia the slaves were not freed until 1968 and that happened under continuous external pressure.
If Mohammed had prohibited any further slavery trading or any more enslaving of war captives as he had forbidden theft, slavery would had come to an end even if he didn’t force people to let go their existing slaves and with or with out that type of (Kaffarah).
According to Dr Kamal Najar in his book “Critical Reading of Islam” (قراءه نقدية للإسلام), Mohammed himself enslaved a number of women after winning the battle with Bany Goridah (بني قريظة) and sent them to be sold in Najid. Such an action would help to enhance slavery business.
I don’t know how reliable the authors sources are but he presents very surprising information. The book can be found at:
http://www.kitabat.com/kamel_alnajar.htm
Check page 32.
If I had time I would have referred to the Sirah Books كتب السيره to check such information. May be some of the members can do that.