It's not enough to own the land and have the political permission from the relevant entity. You also need all kinds of legal permits before you can start construction. And each of those permits provides opportunities for people who don't like the project to sue you to delay or prevent the construction.
In my home country, those lawsuits are cheap and their outcomes are predictable, because they are handled by the administrative court system. The judges are not allowed to consider the substance of the argument. They can only determine if the decisions were made according to the proper processes. Matters of substance are left to politicans to decide.
Here in the US, the lawsuits are handled by civil courts, where judges have more latitude to choose which factors to consider. That makes the lawsuits more expensive and their outcomes unpredictable, which is a major reason why NIMBYism is so effective in the US.
UC is an independent entity from the city and they can build housing on their plentiful land whether locals like it or not.
UCSC just doesn't want to solve the problem and prefers to look the other way and dump the students onto a town that has no space.