The University of Michigan Board of Regents encourages the uniform branding of the satellite campuses with the main campus because it distinguishes them (and has allowed UM-Dearborn, in particular, to attract a higher caliber of student than other commuter campuses in Metro Detroit). Similarly, offering discounted football tickets is a relatively small perk that pays dividends both in attracting students and increasing engagement… those students you’re complaining about may not care about their studies, but they’re not caring in Maize and Blue as opposed to the more active disinterest you see in places like Oakland University or EMU… and is also a benefit afforded to university employees (including, iirc, of the health system). Far more beneficial than getting to take part in the Maize Rage at Crisler periodically, is the benefit of access to UM’s alumni network and library system, which for a serious student makes a branch campus worth it’s weight in gold compared to somewhere like GVSU or even Wayne State. Additionally, I’d note that they simply don’t make enough merchandise branded with Flint or Dearborn to allow alumni of those campuses to identify themselves independent of the general Michigan brand; a coworker whose daughter goes to Dearborn uses a “Michigan Dad” coffee mug not out of willful misrepresentation but because that is the mug they sell on Dearborn’s campus.
I offer a rejoinder: the satellite campuses offer some of the benefits of a Michigan education to an ultimately tiny fraction of the population, who can then do with that what they will. This has no impact on the reputation of the university. Very few people who are not students at the branch campuses going through a cultural cringe have given them or the specificities of their relationship with Ann Arbor any thought. People outside of the state have no idea what the satellite campuses are and are unlikely to distinguish them from Ann Arbor, especially if they are listed on a resume as “University of Michigan, Flint campus” or something, but so? If they excel, that does nothing to detract from the school… and if they fail, it has only as much impact as a poor worker from Ann Arbor.