One of the main reasons they don't want a relationship with you is because they're generally less likely to be persuaded they need to pay more for the improved version of the service, or dissuaded from downgrading/cancelling
Conversely those people that enjoy building a relationship with companies are often those looking to negotiate a discount.
You mention downgrading/canceling... this is the ONE thing you cannot do on any customer service site I've been too. Verizon .. ATT .. Comcast... try to find a "cancel my service" button. You can order new services all day long, but to cancel you've got to call the customer service phone number.
Conversely those people that enjoy building a relationship with companies are often those looking to negotiate a discount.