Also since Google is blocked in China, Firebase Cloud Messaging doesn't work there. Android has something like a 75% market share in that market. Some vendors have their own offerings (e.g. Xiaomi MiPush, Huawei PushKit) etc, I could buy that a popular centralised solution would be more attractive than doing N integrations.
The vision is that you only need to implement support for 1 integration: UnifiedPush, possibly by embedding one of the libraries that manage it and fallbacks. You automatically gain support for compatible alternatives.
There's a variety of reasons why people can't or don't want to rely on Google services. Before UnifiedPush, one would have to "hardcode" an alternative, or more commonly implement a persistent connection within the app.
This also has some potential for more efficient push implementation: for instance, if you have access to an SMS gateway, you could use that to push notification without enabling data connection.
The specification also makes it easier to support third-party operating systems and clients.