Because that is simply not what an interface is made for. An interface is essentially a contract saying “I will provide the functionality described by this interface, regardless of how I handle it internally”. The second part is important because that is the main distinction from an abstract base class. The abstract base class can choose to provide some or all of the functionality itself, but the interface must not provide functionality.
The distinction is important in languages like C# that do not allow multiple inheritance. C++ supports multiple inheritance, but Epic opted not to allow it for UObjects. The reason for this is the same as C#, which is that multiple inheritance complicates RTTI by a lot. On the other hand, since interfaces are guaranteed not to come with details such as member variables, you can add as many as you like without complicating the inheritance tree. It’s a rather intricate topic and an oft discussed one, I recommend reading through Scott Meyers’ Effective C++ if you want to learn more about it.
But with UE4, your best bet would be to either provide this functionality as part of an actual base class or, in the case of an actor, create an actor component.