A small but very interesting observation. Rei's character trait, which makes him please people, is partly a consequence of his upbringing in his family. Judging by the words of Rei himself, the Sakuma clan was oppressed and persecuted in the distant past (probably during the witch hunt) because of its vampire characteristics of the body. And the condition by which the Sakuma could live among people was "to be harmless and useful". So this model of upbringing, which arose from the desire of the Sakuma family to survive, has become just a tradition and a feature of the character of all representatives of this family. Therefore, both Rei, and partly Ritsu, and most likely everyone else from the Sakuma clan have a tendency to want to be useful to others. That's such an interesting thing.
"Because we are harmless and useful, my family was allowed to exist in this world."
"Even in our modern era, when strange things have disappeared, it is difficult to change the way of life that was imprinted in my soul and genes and was fixed thanks to my education."
So these problems of Rei are not only related to his angelic personality (although that too).