[greeneggs]

"AFAIU, Grover's algorithm is not really an algorithm of search of unstructured data, like phone book, but rather a quantum algorithm for inverting a function."

Grover's search algorithm works both for inverting a function and for database search. But if you want to use it for database search, then your database needs to be accessible in coherent superposition, i.e., in some sort of "quantum RAM." For many problems, this probably does not make sense.