I'm not sure I understand why that's invalid.
If you can choose not to show the Home, why would it be invalid to not show the Home only on the blog section of the site?
I understand that in the WordPress structure, the static page is the parent page for everything, but following WordPress structure does not necessarily help a user.
Breadcrumbs are a way to help people position themselves within a website, to know where they are. If you're on a page, then it makes sense that your main static page is the top level parent of that page.
However, if you're on the blog, is it necessary to tell a user that your blog is a subpage of your static page? Or will that just confuse them? I have heard people argue it both ways.
Not saying you should implement this option, but simply that what makes sense internally in WordPress does not always fit a user's experience of a site.
Anyway, thank for the reply. Obviously, since it's not possible, I'll have to think of something else.