The content area itself can't be really inherited in that way. You can't inherit content really. You inherit between page types.

If you have tree structure with:

-Page A (with contentarea property)

---Page B (with contentarea property)

and want the same content in the content area property. 

A few options are:

1. Use fetch-data-from functionality as an editor in Episerver and point Page B to Page A and leave the contentarea in Page B empty. Then it should fetch whatever blocks are present in Page A. Probably not the best solution for a content area but pretty common when reusing content otherwise...

2. Create a block that contains other banner blocks. Add that block to both Page A and Page B when you create them. Since shared blocks are...well shared...if you change banners in the block it will be reflected on both pages. You can of course setup so that that content area, by default, has this block. Pretty decent option that solves the problem without to much custom custom...
If you don't like blocks in blocks, like me, you can use a block that contains a LinkItemCollection that contains the other blocks for instance...

3. Add logic to controller and view instead so that if the content area of Page B is empty, then it should use the content items of Page A instead. I would add this to a separate property in a custom view model and add some custom rendering for it.

Automatic publishing. I would probably skip adding that part. Sound a bit too dangerous if you make mistakes :)