Interfaces and abstract class inheritance, implementation in extended classes

I would consider that you are on the right path. There is no need to declare that you are implementing the interface, when extending a class that already implements it. For me it's just another piece of code to maintain if change is needed. So, yes, you are correct!

Is failure to implement an interface in a child, which is implemented by a parent, considered bad practice or something? Are there any technical drawbacks to omitting the implementation in the child?

I just can't answer your question better than this guy has:

By their nature, although sometimes they may look quite similar, abstract classes and class interfaces serve very distinct purposes.

The interface of a class is meant as a tool for the "user" of that class. An interface is a public presentation for the class, and it should advertise, to anyone considering to use it, what methods and constants are available and accessible from the outside. So, as it name suggests, it always sits between the user and the class implementing it.

On the other hand, an abstract class is a tool aimed at helping the "implementor" of the classes that extend it. It is an infrastructure that can impose restrictions and guidelines about what the concrete classes should look like. From a class design perspective, abstract classes are more architecturally important than interfaces. In this case, the implementor sits between the abstract class and the concrete one, building the latter on top of the former.

Reference

Thus, it's up to you to decide, based on who is going to use (instantiate) your classes, and who is going to write them. If you are the sole user and writer of your classes, then, maybe, just maybe, you don't need them both. But, if you want to give everyone a stripped down to core bits blueprint for the class writer(s) and class user(s), then you should consider using both abstracting and implementing.