Facebook OpenGraph's Image - Can be better

Hi there, at the moment the Facebook OpenGraph's fallback image setting is pretty nice in the sense that there's a fallback image that we can go to should no image be found.

I have been using that setting since I still want to keep my posts' featured images should they have one.

However, if I do "like" my site's root, and not a single post, the first image that is grabbed from my website's index page is not the fallback image. In fact, it grabbed an email icon that I have on my site, which is not really that nice in my opinion.

Due to the above, I'm forced to use the "Always use this image" setting, forgoing my fallback image settings.

Can another setting be added for the website's root/index page? That will be so much better. Thanks.