I got a bit lost. Do you mean that if a product does not have at least the default variant, the entire variant system does not work??? it sounds no sense, as long as it forces me to have and stock for one arbitray variant.
And also, i have never seen nothing related to a default characteristic value in the backend...
By the other way, products with only one variant, a more than possible situation if you delete variants of your inventory, do not display what would be logical: a dropdown with only one option.
Example here:
shoptest.avaray.com/es/component/hikasho...isa_venezuela/cid-67
And still are product that does not display their variants despite having what you anme "default variant", for example:
shoptest.avaray.com/es/component/hikasho...a/category_pathway-0
(which has "M" and "L").