Your image didn’t come through, so I don’t know whether it answers the question – but in case it didn’t let me explain in more detail.
When the image is uploaded in to the library, I can use the text widget on the banner wide when I can copy and paste the url of the image from the library in to an tag but the featured image image is a little different. I don’t want to be doing an tag in a widget for every post, instead, I want to be able to assign something in a widget that says, effectively “when it’s a blog post, use the featured image”
A bit confused here, featured image of every blog post can be shown automatically. You can see here on demo:
If you want to keep image just above the list of blog post then there is way you can do that:
1. Same method given on previous reply. Later you can use widgets visibility module of jetpack to hide/show on specific pages.
2.You need to customize the index.php template. Please proceed for this only if you are technically sound on WordPress otherwise you will be facing same error ie site can be down.