.. I don't think the university does this to produce well-rounded grads, it's to force you to take more classes. This is why it's so much more difficult to finish college in four years now. Nobody has ever cared about what I minored in.
What I am about to say might be viewed as political, but it is really on-topic re: this idea you expressed.
Here's the immediately related part of the idea. I think the people who chartered Queens College had concrete educational goals. They would have created a curriculum and requirements that matched those educational goals within the limits of what was possible and practical at that time. But for the better part of 200 years, I'd imagine the Queens and Rutgers trustees and Presidents and Deans were well-focused on educational goals.. producing well-educated, well-rounded "Rutgers Men".
(this is where the generalization will occur in an attempt to expound on your theory about requiring students to take more classes...)
HOWEVER... over time, and possibly related to agreeing to become The State University of New Jersey, I think all successful organizations take on parasitic entities. These parasites do not focus on the core concrete educational goals. They focus on what's best for them.
Some might say sports falls into this description. But that doesn't really affect individual students' education much.. other than athletes, possibly. Others might point in other directions.. as you say, perhaps the administration just wants students to stay longer, and pay more for that degree. Perhaps some universities force students to take specific social engineering classes (propagandize them). I don't know if this is a real case, but I have read stories where people argue for stuff like requiring students to take classes in equity, etc. Perhaps it could be argued that such required classes produce well-rounded graduates... but that is a fatally flawed argument.
Those examples and more would be signs of parasites capturing an institution and I think that happens everywhere. Let's look at Disney as an example. A man with a vision built a successful corporation. It became so successful, go on to buy ABC and ESPN, Pixar, Lucasfilm, and Fox. Now there is a CEO and board of directors who seem to serve themselves and not the vision of the institution and the whole institution/corporation suffers.
In Olde Queens Tavern I recall seeing a plaque behind the bar or on a wall with a Founding Father-era quote that was something like "if you are successful, expect to be attacked". That is all this is, this thing that I am trying to describe. People doing what's best for them by seeking out successful host organizations. Sometimes it is good for the host organization when goals align.. sometimes it is not.