Leo is most definitely reaching his expectations! Not that the Doctor really had many, because he more than anyone knows just how off history can be. But he can most definitely say that Leo keeps being as great as history says. The Doctor knows another Leonardo of his own universe, and there's basically not much of a difference. They're both absolutely fantastic.

The Doctor kind of sees a lot of himself in Leo. That is, what he would have been if he was a better man. Because Leo is a great man not only in brilliance but in heart and kindness and, well, everything.

Leo is a friend, and a close one. His company is wonderful and heartwarming and his infallible enthusiasm can always be relied upon. He's the sort of person the Doctor would like to be around on bad days because it would make everything better.

Leo is basically just very good and the Doctor loves him.