Students don't vote in city elections for the most part.
The city council represents the homeowners and long time residents. The homeowners want their property values to go up, so most of them oppose more housing. The long time residents inexplicably hate students and "what the students do to this city" despite the fact that the University was there before every single person who live there now.
So the city council does everything it can to keep those property values high, since the students are a captive audience and will rent no matter what, and for the most part don't care what the cost is because their upper middle class parents and/or the federal government is picking up the bill until they graduate.
I personally do my small part by keeping the rent on our place below market, as close to our actual costs as possible. The appreciation on the property value is nice, but the steady income is really what Berkeley property is good for. In 19 years I've had three months of vacancy, and two of those were because I was renovating and one was because my tenants left in a odd month.