I've never understood why it's allowed to give up "suing rights" in contracts. It is in the interest of the public that any law infringement gets investigated and the infringers punished.

In principle a lawsuit is just asking a neutral party to judge whether there indeed was a law breaking where I suspect there was one. Ideally, this is not a inherently hostile action that should be met with any negative consequences.

I know criminal and civil law are different beasts, but still the situation is analogous to renting out a room to someone in exchange for them promising not to report me to the police if I beat them up, else I can kick them out without notice.

It should be an inalienable right of anyone to report/sue for any wrongdoing against them. It should not be conditional on losing some (any) beneficial things.

"I agree I will not sue you even if I later find out that you did something illegal against me" should not be legal to be in a contract.

Giving up such rights is often accompanied by alternative ways of arbitrating disagreement. That's reasonable, as it avoids 50% of the cost (lawyers) in such cases.

I dream of a world where I can present my complaints in plain English and have it considered by a court, without having to pay a fortune to lawyers.

It's somehow an accepted state of affairs that even if you're in the right, you need some cunning lawyers who will twist words in the right way and build a strong narrative of why you are right, otherwise tough luck.

Justice should not be up for purchase.

It's usually not reasonable at all, as whoever does the arbitration depends on the large company behind the contract for continued income, and is therefore strongly incentivized to rule in their favor.