Per the question title, I am trying to make the default template of a page type "inherit". Is this possible?
Just don't select a template and un-check the show template selection!
When creating a page it will result in the settings you see on the right side of the screenshot
If the page type is not set to select page template like e.g. page menu item or there is no default page template, then the default behavior is when you create a page of given type in the tree that it inherits the parent's template.
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