For what it's worth black bands (if you have them given the content being projected) are very easily ignored. Besides, with the rapid advance in display technologies and the correspondingly different implementations of them, it's just not worth getting obsessed about them. Video standards are different than film standards for example.
If you do get obsessed about them, projectors have easily manipulated settings designed to constrain the displayed image to 16:9, meaning of course some of the horizontal or vertical dimension gets lost. Personally I would rather have black bands than lost content.
Designing a home theater can be enjoyable. Implementing a display presentation for a church (both audio and video) involves the same details, minus the architecture.
I suggest that you give strong consideration to the Apple TV 4K - Apple. If you are looking for a projector there are a myriad of considerations. Audio, even more. It's a lot of fun. On that subject I wish Apple would come out with an AVR... but that's a whole other story.