These are called "tagged templates": https://developer.mozilla.org/en-US/docs/Web/JavaScript/Refe...
So if you think about it template strings are like a tagged template who's function just calls .toString() and concatenates each argument it is given. There are some really nice safe sql libraries that use this for constructing queries. They are useful basically anywhere you might want string interpolation and a bit of type safety, or special handling of different types.
Lit Element is also a very clever usage of tagged templates.
(and everybody with a HERE doc implementation that doesn't have that yet should absolutely implement it, people who can't stand perl deserve access to that feature too ;)