Why are college students taught by graduate students in 4-year public universities?

I have never taken a class taught by a grad student and never had a grad student teach any of my classes.  It certainly did not happen in the Cal State or Georgia State system.  I would be outraged and transfer out of any school that shafted me in such a way.

Trust me on this. Those graduate students are eager, and want good evaluations from students to use when they apply for jobs. They put a lot more effort into teaching a lower level course than a  professor who is bored and reads from the same lecture notes year after year.  It would cost universities a lot more to have tenured professors teaching all the classes, which would raise tuition, but this system is also beneficial to the students. In my department, classes are never more than 25 students, and graduate teaching assistants are monitored for quality. Tenured professors are not. 

Not all 4-year universities have graduate students teach courses; not all 4-year universities even have graduate programs and not all departments have graduate programs.  

We have graduate assistants in my department, but it is exceptionally rare that they actually teach a course on their own.  They assist.  Those who do teach on their own are usually advanced graduate students.  

That being said, professors at major universities are expected to devote most of their time to research and grants.  Teaching is not their priority, nor is it expected to be.  They often teach advanced undergraduate and graduate courses.  In these places, it is common for graduate students to teach introductory and lower-level courses.  They are usually closely supervised and well-prepared.  The materials are developed for them and they are coached in delivery methods.  Many of these graduate students hope to become professors themselves, so this is part of their training.

As for classroom size, sometimes that's what is necessary. It's not ideal - no one thinks it is.  But there are a limited number of instructors available to teach, so they may need to offer large sections in order to meet the needs of all of the students.  Exceptionally large lecture halls usually have microphones and sound systems.  A room that holds 150 doesn't usually need that.  If a student can't hear, he or she should say so.  Or he or she should sit closer to the front.

Community colleges have a smaller enrollment, so there isn't usually the need for such large classes.  They offer a limited number of different courses, so they can more easily schedule multiple sections to meet their needs.  Some community colleges offer an excellent education, and they can be a good place for students to start.

Partly tradition, partly price (grad students are cheaper), and partly because "teaching experience" is part of the training for grad students.

The little known secret is that many students are getting a better education at community colleges vs. 4-year universities. This is because community colleges require their professors to hold a Masters Degree, while 4-year universities allow classes to be taught by adjuncts who hold a Bachelor's Degree. Those adjuncts typically work under a senior professor who holds a PhD, but those senior professors almost always teach upper level classes which are not available to the general student population. 

Most graduate students are planning on becoming professors. So they need practice in teaching among other things.     But not all introductory level courses are taught by graduate students.