I have the following XAML:
...
I'm guessing that the writer of Chart, when deriving from FrameworkElement or whatever, failed to realize that they needed to add any child elements to the logical tree either manually or through an override. You don't get that for free when deriving.
Breaking the logical tree breaks the ability of children to bind by ElementName.
If you are the author of the Chart object, you can see this related question and answer.