How do you determine which tenured professors aren't pulling their weight? How do you pull your weight as a professor of some non-employable field of learning? Higher learning isn't vocational training, it's about creating an educated workforce.
If a professor isn't liked by the students and is lagging in publishing, there's a good chance they're mostly dead weight. Likewise, if their peers consider the professor's research worthless and teaching ineffective, they could actually be harmful for the University.
In essence, does the professor still fit the reasons they were granted tenure?
That being said, I don't think that's the right place to focus. I heard that there's a ton of overhead that could be trimmed, such as administration overhead (probably dealing with financials). It would be interesting to compare private and public schools to see what their costs look like and see if maybe we can simplify things to cut costs.
Pubic vs Private? I'm not sure what your trying to say here, there is such a broad range on both sides with a lot of elite private schools having the most expensive tuitions.
I think if you really want to look at how to lower costs you look at how the community colleges do it. Rick Perry (for all that is wrong with that guy) was spot on, when he basically said that it shouldn't really cost much more per year for a 4 year college as it does at a community college. Thats really the key to free college. When people look at Sanders plans, the conveniently forget that we manage to educate these same kids for 13 years without bankrupting the country, adding another 4 years should be a small increase, not a budget busting problem.
