It likely depends on what you consider to be "ads".
Some might argue that the entire website is an advertisement for the university. If you've ever sat in meetings with the alumni association, student recruitment, and the university's "development" department (the people who try to get you to donate money) to redesign the university's website, you'd know how obsessed they are over 'branding' and the like.
But even if you consider them to be a business (even if it's a real estate business that's obligated to teach classes), you'd understand their focus on branding and such. You wouldn't expect to go to ford.com and see advertisements for other vehicles show up ... you might see ads for Ford vehicles, but they want to control their brand. Looking at my alma matter's website just now, I found a few pages with ads for 'online giving'.
It's possible that a school might have a "Code of Conduct" or similar that specifically forbids monetization of web pages, especially if they're a non-profit. There may also be concerns about third-parties harvesting information about their staff and students. If a third party knew who was viewing which websites, they might be able to infer who were students and what courses they were enrolled in ... which may be a FERPA violation. (I'm not aware of any lawsuits / decisions on the matter, this is just speculation).
But we still get into the question of what qualify as "ads". You used to see a lot of groups that participated in "rings" where there would be some topic of unifying interest, and then sites would join the ring, giving links to the other participating sites while getting links back in return. So you had "ads" to link to other thematically linked web pages, but it wasn't like today's ad networks where you had absolutely no idea what might show up on your page.
As has already been alluded to by others, this is bad for the university. If their servers get used for a "watering hole" attack, it could lead to the site being blocked at firewalls for the federal government, which is really bad for research institutions.
You also get the occasional link to a sponsor's page. Usually it's just a text link or maybe a logo and link. You might see this on departmental webpages or various student organizations. There were a number of engineering competitions at my university that I believe all had corporate sponsors (solar car, concrete canoe, baja SAE, etc.)
There will be increasingly higher levels of flexibility and autonomy as you move from the "main" university's web pages to departmental pages & sites to organizations and personal (staff, faculty & student) sites.
These days, if staff or student wanted to monetize a website, it's easy to get external hosting. You wouldn't get shut down when academic computing decided to look into why the webserver was bogged down and found that a staff member had set up a porn site. And you can more easily move your content elsewhere if you control the domain name.
In general, it's just bad form -- does your page exist to give out authoritative information, or to trick people into visiting so that you can try make money off them and try to get them to go elsewhere? Webrings or other link exchanges might make sense in some specific cases, but things like AdSense and such make your website look unprofessional as you lose control over your page. The university provides the hosting, so it's not like you're trying to make your cost back for hosting the pages.
(note: I was the webmaster for a large private non-profit university in the 1990s. I have no idea how many people these days bother w/ university hosting vs. just having a facebook page. And yes, we really did have a staff member put up a porn site. He even worked for our department (night shifts on the helpdesk), and lots of our co-workers had complained about him, but management kept ignoring them)