Your friend are stuck in a stupid cliche. Apart from all the songs already mentioned, don't forget Winter and Moonlight Mile. And there are tons of others.
At the very beginning of his career, I bet he didn't really think he would be such a great singer. To these days, some journalists or whoever still write "he's not such a good singer, but he has incredible charisma..." and this kind of things. They must be deaf then. Or - is it so hard to admit that someone is just perfect
His voice is full of emotinos, full of sex, full of irony...he can express anything, and no one else comes close. And the new album proves his perfectionism. Yes, people who claim that this Jagger is not a good singer should really throw away their prejudice...or envy. He's excellent.