I think a good engine of how restricting permissions to features should be done is the way C360 layouts are assigned. It allows flexibility to limit both on the Currently Logged-in user, but also on Company fields.
It’s important that Success Snapshots have the same features. Filtering by industry, customer type, customer lifecycle stage or any other custom field - all of these things would allow showing only the most relevant snapshot templates in the export selection.
As it stands, unless you want to limit to user groups, which is not a good way to do it on a large scale, you have to show all templates on all accounts.