Object-oriented – Another “Why use Abstract/Interface” question. But I’m a solo developer. Why use it

I'm of the belief that a class should not implement an interface unless that class can be used when an implementation of the interface is required.

BaseWorker fulfills that requirement. Just because you can't directly instantiate a BaseWorker object doesn't mean you can't have a BaseWorker pointer that fulfills the contract. Indeed, that's pretty much the whole point of abstract classes.

Also, it's difficult to tell from the simplified example you posted, but part of the problem may be that the interface and the abstract class are redundant. Unless you have other classes implementing IFooWorker that do not derive from BaseWorker, you don't need the interface at all. Interfaces are just abstract classes with some additional limitations that make multiple inheritance easier.

Again being difficult to tell from a simplified example, the use of a protected method, explicitly referring to the base from a derived class, and the lack of an unambiguous place to declare the interface implementation are warning signs that you are inappropriately using inheritance instead of composition. Without that inheritance, your whole question becomes moot.

A good motivating example for default methods is in the Java standard library, where you now have

list.sort(ordering);

instead of

Collections.sort(list, ordering);

I don't think they could have done that otherwise without more than one identical implementation of List.sort.