Competition is good. Fords make Chevys better. Cadillacs make Lincolns better. Where there are two or more entities in any endeavor each becomes stronger because of the other.
College education is the same. Public education systems become much better because of their need to compete with the private institutions. Stanford is better because of Cal Berkley. Cal Berkley is better because of Stanford. UCLA is better because of USC and USC is better because of UCLA. Utah is better because of BYU and BYU is better because of Utah.
There are no private universities in Nevada. If there were, their mere existence would create competition between those private schools and UNR and UNLV. That would be good for everyone. But, unfortunately, that will never happen.
The only higher education system Nevada will ever have is the one it presently has and that system is not very good. It is difficult to measure the Nevada system’s success when there is nothing to measure it against.