Recording phone calls is useful to suspicious girlfriends, and about nothing else. I doubt any identity thief would listen to your phone calls in hopes that you mention a credit card number or something of value.
Recording phone calls using a trojan app would be useful to anyone who wants to gather information without having to get a legal wiretap: private investigators, unscrupulous reporters, intelligence agencies, organized crime syndicates, etc.
It'd be trivial to sort the calls by listening to a few seconds of each to identify potential high value phone numbers (banks, florists, catalogue ordering lines, etc), then listen to every call to the high-value numbers.