Maybe its the other way around: State governments cut universities' budgets, so universities look for other revenue opportunities.

Big 10 school I went to used out-of-state and foreign students (who paid 2-3x what in-state was) to finance finaid to less advantaged in-state students.

I am not sure about the accurate data, but I feel most universities here in the United States are non-profit organizations (i.e. created not with the goal of distributing excess revenue to members or leaders).

If it is the demand drives up the tuition cost for those non-profit universities, then why not build some for-profit universities here to cater the additional demand?(such as Trump University, or University of Phoenix)

Just because they are non-profit doesn't mean they don't love your money. Just look at the endowment of any major school.

just some side question...if a non-profit organization "loves your money" (which I would interpret as motivated by your money [at least partially]), would that make it not so much a non-profit organization? If that is the case, would this kind of "love your money" behavior exhibited by a non-profit organization make that organization less trustworthy to you?

Or perhaps we could further refine that "love for money" as "beyond necessity" and "within necessity"...but the problem is very difficult for an external observer to tell where the boundary lies for a particular entity -- although that boundary does exist in many cases...

The obvious answer is that "non-profit" doesn't have a meaningful definition outside of the tax code. "Profit" is an accounting trick, for one, so any "excess money" (the commonly-understood meaning of "profit") can easily be funneled into grants, administrator salaries, larger workforces to satisfy administrators' urge to play primate dominance games, etc.

Another one is that "non-profits" (in the tax-code sense) are actually allowed to make a profit (both in the accountants' sense of the word, and the ordinary sense). Hospital systems, for example, often make huge profits, while hiding behind a non-profit status that they've inherited from the bunch of actually-charitable nuns who started running the hospital 150 years ago.

Profit vs. for profit doesn't matter. You need to recruit the right faculty, people at the top of their field who can go anywhere - THAT is the hard problem.