Why do State Universities have such strict entrance policies?

I'm not sure where you are, but they aren't all that strict. For example, University of California only requires a B average and having taken the SATs.

Requirements are to show that a person has the ability to handle college. They also have limited spacing, so they have to have a rational basis for deciding who attends. For some UC campuses and programs, you have to have a 4.0 and very high SAT scores because space is limited and demand is high. It's impossible for them to take everyone and a mistake, since many won't be able to handle the work.

We all benefit when people in society are educated. It encourages businesses because they know they can choose from qualified employees and it brings up the average income.

Community colleges, which are also funded by taxes and anyone over 18 can get into one. (Or under 18 and a high school graduate or in a shared college/high school education program.) They also have overcrowding issues, but they handle that with application deadlines. They also have programs and classes for students who aren't up to college level work.

The states fund post secondary education at all levels, not just University education. Universities have strict entrance policies because if they accept less intelligent students who expect to actually graduate, then they would need to "dumb down" their curriculum. There are still plenty of state Universities where you can be accepted with a 2.5 unweighted GPA and a 1300 SAT. If you can't manage to score any higher than that, then you will not be able to manage university courses and would do much better at a state funded trade school or state funded community college. The states fund post secondary education at all levels, though.

As a tax payer, I don't want to pay the horrendous taxes I do for kids who aren't willing to work their bums off to do well. I sacrifice to make the income I do, and I expect those who are taking my money to sacrifice too. If they're not willing to do what it takes and slack off, then they don't deserve it. Apparently, the state feels the same. Realistically, state colleges often have lower requirements than private colleges, so they do accept those kids who are willing to work, but don't have the educational foundation to be admitted to good private colleges.

There are also community colleges, where in some/many states one just has to be a breathing adult to be admitted, no high school diploma or anything else. The main purposes of community colleges now is to transfer into a state college, so everyone gets a chance at changing their life!

Good luck!