A well-explained perspective, my friend. However, I have a slightly different view. I think both pain and suffering are inevitable and optional depending on the state of mind of the person experiencing them. If pain were inevitable, everyone would feel pain the same way. Some people handle pain better than others, and some can become numb to pain through meditation.
If suffering were optional, many would choose to opt out of it instead of committing suicide. The mind believes what it believes, and what it believes as inevitable is inevitable.
The theory of life as suffering can be both accurate and flawed. Physical life is neither suffering nor happiness. However, spiritual life can be about suffering. Humans have to overcome life's challenges to survive its conditions.
Have a wonderful day ahead, my friend.