Removing the dead happens, but when people die of an infectious disease, it's generally not a good idea to go on as usual and let everyone and their mother touch the dead person. Just to be clear: not blaming the people there for still being far behind in hygiene in situations like this, but it did make it very much easier for in this case Ebola to spread.
The biggest Ebola epidemic didn't start in a local market by the way, it most likely started because of a young boy coming in contact with a bat in some tiny village, after which his sister, mom and grandmom got infected and died, and then it spread.