Avrohom Avinu Did Chesed on His Own:
Rav Meir of Premishlan zy”a explains Rashi’s words by saying that since Avrohom Avinu enacted the prayer of Tefillas Shacharis, he davened right at the beginning of the day and was then free to welcome guests all day long and to spend his entire day caring for their needs. Through this, Hashem’s name became known in the world.
Avrohom specifically wanted to wait on his guests on his own, rather than having someone else do it on his behalf, because one gets a bigger mitzvah when he does a good deed on his own. Yitzchok Avinu, one the other hand enacted the saying of Tefillas Minchah. Rav Meir of Premishlan understands this to mean that he davened all day until Minchah time. Therefore, he had an agent take care of his guests on his behalf until then. Yaakov Avinu enacted the saying of Tefillas Arvis, which means that he davened all day until Maariv time. Therefore, he also had to do hachansas orchim through an agent.
For this reason, Hashem said that the bracha would end only with Avrohom. Since he would only do the mitzvah on his own, he personally glorified Hashem’s name in this world. In return, Hashem glorified his name by having the bracha conclude only with him.
