Rabbi Eli Monsour asks an important question. From DailyHalacha.com:
Many Rishonim (Medieval sages) raised the question of why the Rabbis did not ordain the recitation of a Beracha over the Mitzva of Bikur Cholim (visiting the sick), as they did for other Mitzvot. …
The Rashba (Rabbi Shlomo Ben Aderet, Spain, 1235-1310) answers this question by establishing a basic principle regarding the Berachot recited over Mitzvot. He claims that the Rabbis did not ordain the recitation of a Beracha over a Mitzva whose performance depends upon two different people. Tzedaka, for example, requires the participation of both the donor and recipient. If a person would recite a Beracha before giving charity, then if the poor person refuses the donation the Beracha would become a "Beracha Le'vatala" (a "wasted" Beracha, which is forbidden to recite). Similarly, if a person recites a Beracha before entering the patient's room to pay a visit, and the patient asks him to leave, his Beracha would be "Le'vatala." The Rabbis therefore chose not to ordain the recitation of a Beracha over these and other Mitzvot that depend upon the consent of a second party.
The Or Zarua (Rabbi Yitzchak of Vienna, 1180-1250) suggests a different reason why no Beracha is recited over the Mitzva of visiting the sick, claiming that no Beracha is recited over a Mitzva that can be performed at any time.…
Others suggested that the Rabbis did not ordain the recitation of a Beracha over Mitzvot that are intuitively logical, which even the gentiles acknowledge.… [E]ven the gentiles – who were not "sanctified with His commandments" – acknowledge and perform this Mitzva.…
I find these answers weak, and was happy to see that Rabbi Monsour suggests what I also belive to be the correct – and the obvious – answer:
We may suggest an additional reason, namely, that it would be inappropriate to recite a Beracha over a Mitzva that presents itself as a result of the pain and suffering of another person. As a person enters the room to visit his ailing friend, he should not joyfully express his gratitude to God for enabling him to perform this Mitzva, which came about because of another person's pain.
This seems so obvious, I wonder why Rishonim did not mention it. Readers? Any thoughts on this?