Am I allowed to have “incomplete” aggregates in DDD?

Question

DDD states that you should only ever access entities through their aggregate root. So say for instance that you have an aggregate root X which potentially has a lot of

Answer 1

You're really asking two overlapping questions.

1. The title and first half of your question are philosophical/theoretical. I think the reason for accessing entities only through their "aggregate root" is to abstract away the kinds of implementation details you're describing. Access through the aggregate root is a way to reduce complexity by having a trusted point of access. You're eliminating friction/ambiguity/uncertainty by adhering to a convention. It doesn't matter how it's implemented within the root, you just know that when you ask for an entity it will be there. I don't think this perspective rules out a "filtered repository" as you describe. But to provide a pit of success for devs to fall into, it should be impossible instantiate the repository without being explicit about its "filteredness;" likewise, if shared access to a repository instance is possible, the "filteredness" should be explicit when coding in the caller.

2. The second half of your question is about implementation on a specific platform. Not sure why you mention delayed execution, I think that's really orthogonal to the filtering question. The filtering itself could be a bit tricky to implement with LINQ. Maybe rather than inlining the Where lambdas, you set up a collection of them and select one depending on the filter you need.