The gemara says that for Ner Chanukah there was a bracha of she'asa nissim instituted on the seeing of the mitzvah, even without actually performing the mitzvah. Rashi implies that so long as one has not yet lit ner chanukah, they make a bracha on the seeing of the ner lit by someone else, even if they intend to light themselves later that evening. Rashi in Shabbos is explicit about this. However, we follow the opinions that the bracha on seeing was only instituted for those who don't intend to light themselves, and don't have people in their household lighting for them.
Tosafos asks why chazal did not institute a bracha on seeing any other mitzvah, and only instituted a bracha for the seeing of Ner Chanukah. It seems that Rashi was also bothered by this question and tries to address it. Rashi writes - ורואה אותה בפתחי ישראל שמצוה להניח בפתח, צריך לברך על ראיה הראשונה. Rashi seems to add a superfluous line - שמצוה להניח בפתח. Simply, Rashi is just explaining how one happens to see the Ner lit by someone else when just passing by on the street. However, it seems to me that Rashi is trying to say that lighting in a way that it is visible from the street was part of the ikar takana of ner chanukah, therefore when one sees the ner chanukah of someone else, chazal instituted a special bracha. For other mitzvos where the publicizing was not part of the ikar takana, chazal were not mesakein a bracha on merely seeing it.
Tosafos offers three answers to this question. 1. Due to the חביבות הנס and inspiring love for the miracle, they instituted a bracha on the seeing of Ner Chanuka. This would not apply to mitzvos that don't directly represent a Neis. 2. Many people don't have homes of their own in which to light Ner Chanuka, therefore chazal instituted a method of connecting them to the mitzvah by making a bracha on the seeing of the candle. 3. It only makes sense to institute a bracha on the seeing, if when actually performing the mitzvah, one would also make that bracha. Since there is no bracha of שעשה נסים made on taking lulav and sitting in a Succah, there is no bracha made on the seeing of it.
Tosafos rejects the second answer by saying that it is difficult from mezuzah. Meaning, if chazal were worried about one who doesn't have a house being unable to perform this mitzvah and therefore instituted some connection to the mitzvah, namely to make a bracha on the seeing of the Ner, they should have instituted a bracha on seeing a mezuzah as well, to accommodate for those who don't have homes to hang a mezuzah.
This question of Tosafos is very difficult to understand. It seems that there is a fundamental distinction between mezuza and ner chanukah. One who doesn't have a house is patur from mezuzah. In other words, mezuza is a chovas ha'dor, an obligation on one who lives in a house. The house is the me'chayev in the mitzvah. Without a house there is no obligation to do the mitzvah at all. One is certainly not compelled to buy house to perform this mitzvah. However, the mitzvah of ner chanukah is a mitzvah on the individual, just that one needs a house to have a place to light. One who is missing a house is still technically obligated in the mitzvah, just that they have no ability to perform it. It is as if they are handcuffed to a pole and therefore unable to take lulav. Therefore, it would make sense that for such a situation chazal would institute a possibility to at least connect to the mitzvah and make a bracha on the seeing of the Ner.