While something like what you two are talking about would be useful, I think it’s better suited for another custom project or as a feature request to core. Custom Header doesn’t render markdown and it’s not something I’d add. There is no need for an !include for header text as it’s global from the get go.
Ideally someone with more time than me might make a custom card, one that inserts a card to the top of every Lovelace view. Wouldn’t be that difficult, could allow for the “pinned” card to be defined once, and would be infinitely customizable as it would just accept any Lovelace card (or cards if used with stacks).
CH already suffers from feature bloat and I think something like this is outside the scope the project.