My parents did that for years with The Boston Globe. Every August, they'd quit, and every September, they'd pick up a new 1-year introductory subscription at about 1/3 of the price.
I've been trying to get them to do the same with phone/Internet service - my Comcast is about half as much as their Verizon because I'm on a promotional 1 year subscription. Hell, just quitting FIOS, using dialup for a month, and then buying the exact same subscription they already have would save them $10-15/month.
Similar perverse incentives are at work in the job market (you usually get much better offers by changing jobs) and the housing market (apartments tend to jack up the rents as much as possible on existing tenants while offering move-in specials to new tenants). And people wonder why there's no loyalty in America anymore...
A good tactic when possible, but Comcast requires a 3-month away period to qualify as a new customer. I think the best tactic is threaten to quit, if that doesn't work then phone back another day and try your luck again with the call center lottery.
Though you can do like I did. Call to cancel cable, and they reduce it by half bringing your total package of cable/internet to a more reasonable price. I guess they have a greater fear of showing declining subscribers than sticking to their (outrageous) price.
(Sidenote: you know you have been in Japan too long when you spell it colorrary and wonder why the spellchecker flags it. sigh)