Promoting herbal medicine

Sorry to break it to you but they don't work.

Ayahuasca Harmaline "proven" to kill cancer? I doubt it. Chemotherapy remains the best solution for cancer.

Both are study that's limited to the effects on cell cultures. It's a far leap to conclude that this is the cure for cancer. In vitro's limitations are in a very specific and limited environment that doesn't match the reality of the human body. They can be good pilot studies, but you can't say it's a "proven" cure for cancer, and it's very disingenuous to imply that "the man and pharma" would be bankrupt out of their asses if they let people knew about the secret alternative cure, which I've seen this argument be repeated extremely often by alt-med promoters.

"Alternate research", no, that's just a nice way of saying research that isn't widespread because of reasons I listed previously. I strongly suggest against any other treatment, especially when this one isn't used as treatment because the studies you're showing me is already quite limited in scope. Chemotherapy turns people into vegetables, but it remains the best method to treat cancer, and I believe promoting alternative medicine for cancer is dangerous and expensive.

Chemo is unpleasant. I know this. I've had a best friend irl who suffered from leukemia and I was very difficult experience for everyone involved. He had to suffer losing hair, nausea, and the pain of bone marrow transplants. He remained committed to chemotherapy, however, as it remains his best shot at survival, and he's recovered today, and I do hope the leukemia doesn't come back. If he or his family decides to forgo chemo, I think the outcome will be far worse.

It's this case, correct
https://en.wikipedia.org/wiki/Ashya_King_case

Refusing chemo for your child is usually not the right choice. I don't know the details of the story but I'm sure there's a reason they're filed abduction charges. I'm aware that proton therapy appears to be used as conventional treatment but I fail to see how it will replace chemo, and it also comes with its own risks and harms as well as also being really limited in application. That the boy survived seems to give too much credit to proton therapy. In the Wikipedia article, he had medulloblastoma that was successfully removed through surgery and he also received more surgery, which I suspect contributed to King's recovery.

In this case the doctors did not support moving the boy so that he could get proton therapy, and in response, on 28 August 2014, the parents took their son out of the hospital without telling the medical team and boarded a ferry to France.

Yeah, disobeying the doctors like that is dangerous. Again, it's good that King survived, but this endangers King's life. In fact this reduced his chances of survival from 80 to 50 per cent.

https://www.telegraph.co.uk/news/nhs/11749505/Ashya-Kings-parents-reduced-his-survival-chances-by-30-per-cent-report-reveals.html

There's a ton of head-ache inducing conflict and miscommunication in that article.

Proton therapy also has its own issues.

The issue of when, whether, and how best to apply this technology is controversial. As of 2012 there have been no controlled trials to demonstrate that proton therapy yields improved survival or other clinical outcomes (including impotence in prostate cancer) compared to other types of radiation therapy, although a five-year study of prostate cancer is underway at Massachusetts General Hospital.

https://scienceblog.cancerresearchuk.org/2013/09/16/proton-therapy-is-coming-to-the-uk-but-what-does-it-mean-for-patients/ <- link right in the Wikipedia article you cited

Before we get too excited about this new treatment, it’s important to point out that it’s thought that only around one per cent of UK cancer patients could be suitable for proton therapy. There’s also a lack of hard conventional evidence to prove that it’s more effective and kinder than conventional radiotherapy.

Further research isn't being "suppressed". As I pointed out, evidence is either limited or low-quality.

Chemo saves lives. Alternative therapies do not. The boy had a higher chance surviving if he had chemo. While I don't think the government should've went into a manhunt to King's parents (I think there is a gross misunderstanding going on), his parents did the wrong thing and were lucky that their son survived.