Possibly it would be an incentive that is not aligned with the user's interests. For example, CCC would do anything in their power to get you to buy something so that they get a cut. Whereas a user would maybe be most interested in getting a good value, or even not buying anything at all might be their best choice.

Of course you as a consumer could also act and decide on your own.

I'd understand if the grand parent poster refused to use price alerts at all, maybe in order to avoid unnecessary purchases, but GP argued that a different service is better because it doesn't use affiliate links, which seems rather strange to me. After all you get an alert for a product you chose at a specific price you defined. The use of affiliate links doesn't change anything in this arrangement.

Possibly out of privacy concerns?