Zombies have the issue that they aren't a real threat to society anymore. Even if they can sprint, modern weapons just make them too easy to deal with. So you can have the initial stages of the main characters making it to safety, which is commonly included in Zombie media. But then the phase from initial outbreak to collapse of society can't be explained, skipping it is way easier. You would need to go rather unrealistic ways to explain the collapse but the genre kinda lives on the plausibility of the events. World War Z for example can't be taken seriously. That doesn't necessarily mean it's bad but it's a different kind of genre.

Then you also run into the issue of the initial stages being rather boring. If a big part of humanity died rather quickly, there is an abundance of resources for those remaining. Looting a single supermarket would give you enough food for months or years. And anyone semi-intelligent would just hunker down somewhere safe. It's easier to create urgency if there is a lack of resources.

This also applies to many other apocalyptic events. Either humanity dies out almost immediately or the collapse becomes hard to explain.

You would need a slow moving apocalyptic event to show the collapse of humanity. Something like climate change. But then it's more interesting to focus on other parts rather than the survival of the main character. So we end up with a different genre.