I think there is a good reason it does not exist: the legality of non-consent. A lot of states require consent from the person being recorded. If say somehow this app exists and you have that app, then for every phone call that comes in that you answer, you will have to say "this phone call is being monitored and recorded." If the person that calls does not consent to being recorded, the call must end.
I can totally understand having such an app for businesses or if you are getting calls from collection agencies or harrasing people/companies. But just keep in mind even if someone like a friend or family member is calling you, you will have to get their consent