I can spend the rest of the day providing examples of cases of a palliative care intervention saving someone from saying they wanted to end their life earlier.
I worked for a few years in Switzerland, and one particular case comes to mind. A young man with advanced lung cancer came into the hospital in Lausanne saying that he couldn't live like this, that he wanted to end his life, and that he had the right of access to assisted suicide. We got the palliative team involved, controlled all his symptoms, and a few days later he went home again. He published a story in the newspaper saying that it helped him, because he could now spend quality time with his family.
I totally agree with your saying that if there is no palliative care, then there isn't any choice. Palliative care does make a difference for the overwhelming majority of people.