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: 
Hmmmm... It seems like that could be something to consider doing when our group is larger, but right now it's not as though we're getting so many entries that it is overwhelming. My concern in adding a theme is that we'd cut the number of entries in half if a theme were introduced. 

There's also the notion of who comes up with the themes? Would the mods be in charge of coming up with something, or would someone need to maintain a weekly thread for voting on the theme like we already do for the picture? Sounds like adding quite a bit more admin work to something that really works fine as it is...
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.