The one being paid is the teacher, and the one being provided a service is the student, so really the students should be grading the teacher and not the other way around

Except primary education is compulsory. Many students simply don't want to be there. Students of a certain age are also not competent enough to really evaluate an educator. I've had educators in my past that at the time I would have 'graded' poorly but over the long run their lessons landed and I saw the value of their methods.

she grades them based on her feelings and speculations of what a good student is, not on whether they are actually productive in some way.

Any teacher that does this is a shitty teacher. If you went to schools with teachers like this you went to bad schools. The whole point of schooling is grading pupils on merit. You're not seeing the full picture of what modern education has become. The autonomy of teachers is being removed for political and financial reason and most lessons, discipline procedures, etc are coming from top down. If you have a school with an unfair grading system it's almost always a top down problem. Hiring has become political.

Grades create hostility between the student and the teacher.

There's two possible reasons for this. You were raised in a family that hates traditional meritocratic ways of viewing the world (very common in female households), or you have teachers that are failing to establish clear objectives and access you in a fair way. Grades are suppose to simply be a reflection of your progress in a course. If you're serious about learning a skill or trade you will crave quality feedback. Would you want to pay good money for a college class and not know how you are progressing on the content? Is the professor really doing his job if he's just delivering knowledge and not also giving you feedback on your acquisition of said content? All merit and growth mindset people crave feedback because feedback drives growth faster.

Grades are an infinite resource which teachers are given the authority to deprive their students of

This doesn't make sense. It almost sounds like you've been propagandized with Marxist dogma and you're approaching everything from such suppositions. Marx saw the world from an 'oppressor vs oppressed' lens. For Marx all conflict came from that poison tree of one group exploiting another. The views of Marx aren't all wrong but when his core philosophy corrupts your soul it can make you dehumanize others and it can make you disregard more classical (and logical) explanations like supply and demand, hierarchy, etc.

when really it would be better if the teacher were a friend.

Teachers are not allowed to be friends with students due to some fairly complicated factors. We live in a modern world full of litigious assholes that sue at the drop of the hat. Our legal system is set up to help lawyers, insurance companies and LLC's almost exclusively. Everyone in modern education and any other field that deals with children are terrified of being sued so there's this heavy influence to keep employees from really closely interacting with their 'customers'. This isn't just in education.

Another big problem is that young people today have a serious entitlement problem. This isn't new. My generation had it, but it's worse today. This entitlement syndrome makes young people think that they can only learn from someone that they have a relationship with. Which is a shame. Some of my greatest coaches and teachers were people I didn't like and I wasn't really friends with. Luckily I had parents that taught me you respect the job title not the person. You can learn from anybody. You don't have to have a relationship with them to learn. This advice helped me in my life. It kept me from the nasty habit of making 'excuses' when I was struggling in school or sports. Most of the time people just can't hang with the rigor of the class or the sport and they find excuses so that their psychological bubble of safety stays unbroken. Unfortunately for these folks they will never know greatness. Greatness lies way out past the threshold of our snugly safe space.

In my opinion, grades assigned by a teacher should be totally done away with. If universities want a way to decide which students to admit, they should simply hold entrance exams.

Your wish is already being granted. This has been a trend in education for at least a decade.

If universities want a way to decide which students to admit, they should simply hold entrance exams.

If you take the 'anti grades' logic far enough though you will start opposing entrance exams as well. Entrance exams have the side affect of excluding students that get low grades. Funny how that works.

Why do colleges even take high school grades seriously?

How else are they suppose to be exclusive? College is suppose to be a place to give people a higher level of training in certain fields. You can't bestow that certification if you have no screening process for who comes into the school. Granted I personally very very negative about the state of our current college system but that's a different comment for a different thread.