There are numerous - too numerous - explanations of Korach's wrongdoing. In fact, one man's Korach can be the next man's Moshe. Nevertheless, we can rather safely say that Korach was anti-establishment even though, as a cousin of Moshe and a Kehatite, he was on the fringes of the establishment. Moshe's response of "rav lakhem benei Levi" may indicate that he felt that Korach's "rebellion" was insincere, merely a ploy to gain popular support. Chazal pick up on this by considering Korach's dissent "not for the sake of Heaven." Yet the critique may have in fact been a solid one - and if not in that generation, then in a later one.
Chazal view the prophet Shmuel as a descendant of Korach. Some read Shmuel as a tikkun for Korach because he established the monarchy and helped make plans for Jerusalem (I remember hearing such an idea from R. Kalman Baer of KBY). Yet Shmuel can also be read as a continuation of Korach's anti-establishment and populist revolt. He reforms the Israelite leadership and travels around Israel instead of remaining at a single holy site (I have four previous posts on Shmuel as the synthesis of Eli's establishment with Chana's rebellious streak: [here, here, here, and here]). Thus, even if we take a view of Korach that is wholly negative, we may still believe that his critique remains valid in a different context. His call for equal opportunity, an end to nepotism, a meritocracy, or transparency may have been a misguided political stunt, but that need not mean that such a critique is always irrelevant.
Which leads me to my modern-day Korach, Rabbi Benny Lau. As his name indicates, he is a "blue-blooded" rabbi, a nephew of former Chief Rabbi Yisrael Meir Lau and a cousin to several "rising stars" within the Rabbanut - including the rabbi of my own city of Modiin. Yet Rabbi Lau has consistently called for the reform - I have personally heard him call the Rabbanut "passe" and express a wish that it be totally shut down. He has written the following (HT and translation by: Menachem Mendel):
We have arrived at an ugly abyss of hanhagah haredit and our only option is to rebel against it: this is not our Torah, this is not our worldview, and these are not our sages. Our children need to hear us rising up against the violence and the silencing. We need to shout at the top of lungs: this is not the way of the Torah! We believe in God and His Torah and refuse to bow our heads before this evil papacy. We must strengthen one another in believing in God and His Torah and to strengthen our belief in the uprightness and goodness of all of our children.[MM points to similar sentiments from R. Lau here as well].
These are clearly Korach-esque sentiments, coming from the very family of the hanhaga haredit that he calls for a rebellion against. Yet unlike the original Korach, the contemporary application is apropos and, from what I can gauge from the few times that I've met R. Benny, wholly for the sake of Heaven.