Why? Its supposed to be taking place before the pandemic takes hold, so life would be normal for the vast majority of people. Doing it this way we get to see how the family and the rest of the world is affected as the zombies start to get noticed right through to full blown zombie apocalypse.
The zombie craze has already peaked ages ago, so they need to find a different angle, a straight forward copy of TWD would be a waste of time. Because of the way we were just dumped into the zombie apocalypse with TWD, there is a lot of interest in how it unfolded, more of a back story and FTWD is an opportunity do tell that story.