What is the significance in Judaism of wearing 19th century clothing? Don’t tell me that it’s specifically “Jewish” or “rabbinical” clothing. These wide-brimmed black hats and frocks with the long slit down the back that the rabbis and Yeshiva people wear are obviously nothing more than gentile styles that were in vogue in Western culture in the late 1800s, and differ in no way from the daily business suits worn by Ulysses S. Grant, an anti-semitic drunkard. If there was an issue of wearing specifically “Jewish” styles, wouldn’t it make more sense to wear what archaeological findings have shown to have been the kind of clothing our ancestors wore in Israel in the time of the Temples? I am aware of the fact that this clothing is not as popular in the “national religious” community as it is in the “Chareidi” one, and that you pride yourselves with the “Kippa Sruga” image instead of the “black hat” one. But even in "national religious" society, although the laity, the Yeshiva students, and the low-ranking rabbis do not, the highest achievers, namely, the high-ranking rabbis, do wear black hats and suits, and often frocks, which seems to indicate that even you people agree that wearing such clothing is, in fact, the IDEAL situation, and that the lower-ranking members of your society who do not just “haven’t gotten there yet”. Also, it seems to be a subtle admission on your part that the Chareidi society as a whole is on a higher level of religiousity than yours, since a religious custom practiced in yours by only the highest ranking members is practiced in theirs even by the lowest ranking ones.
Wearing a particular style of clothing and not another when both are acceptable from the point of view of modesty is a matter of social identification rather than Halacha. It is understandable that a student might want to dress like his Rav to demonstrate that identification. That rabbis in Israel- even those who identify with national-religious ideology- often wear the black clothing you describe is similar to a doctor wearing white: it's a "uniform" that informs people of his position. PS Your description of General Grant is not universally accepted. When Lincoln was told that Grant had a drinking problem, he asked that his other generals be given the brand of whiskey that Grant was drinking.