Question: I would find it more interesting/organized if there was a theme to follow for the featured images each week. For example, this week post only pictures of cars, flowers, landscape or whatever and change the theme every week.

Answer: 
If we ever did end up using a theme week, I'd like to suggest that we have a "un-edited" week, so the challenge would be to get the best photo out of your camera. Many of the photos seem to have a lot of post-processing. I'm not suggesting this is bad - the photos are stunning - but I bet there are a lot of excellent photographers out there who are not necessarily photo-editing gurus (or is that now a required skill to be a good photographer?).
The contest idea, this is similar to many photo sites I am familiar with in the past. 

Personally I don't typically have time to go out and shoot the theme every week, so I would likely participate less if ever.

It does have some merit to expand your portfolio or challenge one, but it's just not my favorite way to shoot or think about shooting.