A very good question. The short answer is that it is not known if the use of convalescent antibodies (or convalescent serum) is effective with Ebola. But since there is no effective treatment for Ebola, doctors have resorted to still-experimental treatment, but that is at their discretion. Zmapp or the drug by Tekmira would be other examples of still experimental treatments that have been tried.

This case series from a prior Ebola outbreak indicates that a transfusion of convalescent serum shows promise. However, the article does mention that animal experiments did not show effectiveness.

Another mainstream article about this topic is this one.

Donors must meet a number of criteria according to the WHO guidelines. Age 18-60, must wait 4 weeks since discharge and have two negative RT-PCR tests for Ebola, plus be screened for a number of diseases like HIV and hepatitis. The usual blood typing rules between donors and recipients also applies. Anyway, all these criteria limits the donor pool even further.

But putting aside the effectiveness question, I'm not sure that there are enough trained personnel or equipment to do this procedure properly in most of the regions in West Africa where Ebola is raging. There aren't enough resources to give people even basic nursing and supportive care. You also need survivors of Ebola to get the antibodies from and unfortunately, there aren't that many in this outbreak.

It seems that Dr Kent Brantly is giving a lot more transfusions than guidelines would recommend. Kudos to him for his generosity, but that's likely not going to be feasible among most West Africans donors either.