Sure, but people who commonly tout it's "not one disease" miss the broader point of the common nature of the disease(s).
The classification of "being a cancer" does imply (rightly) that there are similarities. The question is if this helps us in treating the cause or not.
I feel that perhaps saying "cancerous diseases" is clearer than saying "cancers".
a) The corruption cannot be repaired;
b) The cell still survives;
c) The mechanisms that normally regulate cell division are impaired, causing the cell to continually divide.
d) The daughter cells also have DNA corruptions with the same properties.
Of course, depending on the nature of the DNA corruption and on what cells were corrupted, the resulting illnesses may be vastly different, as well as the strategies to combat them. But couldn't you at least look for ways to prevent cancer universally if you somehow address this common cause?
The thing is, your given (some event corrupts the cell's DNA) needs to be examined. Let's agree that some event corrupts the cell's DNA as you suggest, and then follow up with some questions.
1) Where in the enormous strand was it corrupted?
1a) Was it one place, or several?
2) What corrupted it?
2a) Again, was it one cause, or five different causes, three of which we don't know about and can't currently track?
3) Does the mechanism of action (the thing that caused the mutation) change the way a specific pathology progresses, even if it's a similar mutation in the same area? (yes)
So that's sort of the problem with cancer research. They're not trying to solve a single problem with a bunch of different presentations, they're trying to solve a fuckton of problems with a similar number of presentations, some of which are similar even though they have different roots.
I would argue that it's not. People use 'cancerous' as an adjective describing things that aren't cancer all the time. Of course, if you're only using 'cancerous' to refer to cancers (I.e., in the context of pathology,) then just call them cancers.
Therefore a benign tumor is much closer related to a cancerous tumor that to leukemia.