It seems that your problem is that you map the aggregate and the view the user wants to see 1:1. Solely because we talk about an aggregate it's not 1:1 the view. (you said it by your own "but in most cases the customer only wants to see a small part of the aggregate").
A benefit of using CQRS (or "only" CQS) is that you can concentrate on the domain, means you can model you commands and views (e.q. query) from the user/customer perspective, disregarding you current database design.
Take a look at effective aggregate Design by Vaughn Vernon, possible it helps.