I'm assuming you've also observed some covariates for each customer beyond whether or not they canceled. Your suggested approach, then, would simply give you 4 groups of customers who canceled that are similar in terms of those other covariates. You could then examine the characteristics of those groups to see if they merit different retention strategies based on marketing theory. However, this would be a somewhat ad-hoc approach.
A more statistical way to approach the question would be this. First, can I tell which covariates determine whether or not a customer is likely to cancel? A logistic regression model could do this, for example. If you then suspect that customers who differ on a certain covariate $X$ are likely to cancel for different reasons, then you could include an interaction between $X$ and other covariates in the logistic regression model.
For example, suppose you're selling newspapers and you observe $Y =$ cancellation, $X =$ political affiliation (Democrat/Republican/Independent), and a measure of "liberalness" of the news customers read on a 1-10 scale $Z$. Then you might run the regression $Y \sim X + Z$ and conclude that Democrats are most likely to cancel but that liberalness doesn't really affect cancellation much. But then you might run the regression $Y \sim X + Z + XZ$, which includes an interaction term, and realize that higher liberalness decreases cancellation probability for Democrats, doesn't change it for Independents, and increases it for Republicans.
You might then conclude that you need to target your paper's articles more aggressively to the politics of its readers, which would be good for your circulation but probably bad for society.