Why do so few artworks of the Early Byzantine Empire still exist today?

One reason for this was that the buildings were later changed and rebuild - this is a reason for why surviving architecture from this time is rare.

However, I think the question is leading us to the topic of iconoclastic controversy - in 8th and 9th century people believed that the portrayal of religious icons was inappropriate and frequently destroyed earlier religious works.

So the answer is: they were destroyed in 8th and 9th century.