Narrow to a sparse tree?

Question

There are times I prefer to work in a sparse tree instead of an agenda, namely ease of quick edits.

However the sparse tree, even with all folds level set to on (e.g. org-show-siblings and others), still the tree still shows tasks/headlines in a folded state. I would prefer them to be entirely hidden, just like org-narrow-to-subtree (C-x n s).

This only works with a single subtree. Is there a way to extend the narrowing to all of the sparse tree, and completely hide the non-sparce tasks/headlines?