Yes? There are lots of variations of cancer, but it seems to be a well defined set of conditions. I don't think I've ever seen an argument over whether something is or is not cancer, or suggestion that such an argument could be made.
Our current methods of treating it treat it in a piecemeal fashion, targeting one variation or another, but I don't think it's unthinkable that you could managed to target and fix the entire set.
Set is an understatement here, there are about ~200 types (as of now), and within a numerous amount of mutations per person. This is why one person could have been treated effectively with early enough detection, and others it just keeps spreading despite treatment. What's even worse, even if treatment does work, it can eventually stop working due to these mutations.
This is why we deal with it piecemeal, because it's the only way we can actually detect it. This isn't a current technical limitation, this is a "we can't solve something before we know the problem" issue due to how cells work. Even in the very long term future where we have bio implants, the best solution we would have are implants being able to seek cancer cells instantly and remove them.
Humour me for a second and think about this in a "sci-fi we have whatever theoretically possible technology we want" fashion.
Suppose scanning technology progresses to the point where we can quickly resolve every cell in the human body. Suppose computing technology progresses to the point where we can quickly interpret that scan data and identify which areas are normal and which areas are tumorous growths that shouldn't exist. Suppose surgical(/point application of energy) technology progresses to the point where we can destroy any individual cell without collateral damage.
I believe at that point we could solve the entire set of conditions called cancer (but maybe not all disease, maybe some forms of dementia still evade us for instance).
I'm not criticizing the current approach by calling it piecemeal. It's what we know how to do, doing it saves lives, of course we should do it. I'm just saying that cancer is a meaningfully label, and it's conceivable that at some point we can solve it, all of it.