According to the law, yes. They absolutely deserve that money because that's what the law says. You can't choose to ignore a law because it's inconvenient for you. If you choose to ignore a law for your own benefit then that allows others to do the same for your potential detriment. That's extremely bad short-term thinking.
Your complaint is with the law, it has nothing to do with the content providers. You say but the content providers influence the law with money. In that case your complaint is with the system that writes the law. Your ire is misdirected and likely will cause nothing to change.
Of course, there's civil disobedience to consider. It would be an interesting way to combat the laws at hand but I'm not sure how to go about that in terms of media consumption. I suppose if enough people did it at the same time.
But you fall into the common problems with these type of discussion; you act as if your choices are limited. For instance, with piracy it's usually "they don't make it easy and/or cheap enough for me to buy so therefore I must steal it" which is a self-limiting range of options. It totally ignores several options such as simply not consuming the content in question and move on to something else. You present only one option in your desire to create, a derivative work based off of another's content. That's not your only option in this case.
Finally, this idea that this stuff is a part of our culture and we're locked out of it. I would say if we're locked out of it so tightly that we can't enjoy it then I wouldn't call it part of our culture. But this culture defense is new to me in these terms, it's an interesting idea. It will ultimately fail in the end but an interesting defense nonetheless.