thing is, in practice it gets used as a type. If you repeat that function definition more than once you are creating a bit of a nightmare to maintain.
For instance if you need to add an extra parameter, you can easily find all usages. If something else uses the same definition, but is used for a different purpose, it gets much harder to distinguish the different usages. especially for a good ol void (callback)(void context) which a number of event's may use, and then later some may callback with more information which can be changed in once place and the compiler will quickly show you what breaks.
For instance if you need to add an extra parameter, you can easily find all usages. If something else uses the same definition, but is used for a different purpose, it gets much harder to distinguish the different usages. especially for a good ol void (callback)(void context) which a number of event's may use, and then later some may callback with more information which can be changed in once place and the compiler will quickly show you what breaks.