Nintendo tends to just this, actually. It makes good business sense as console companies tend to make a lot more money on games than consoles (and initially Sony's strategy was to lose money on the console). Assuming it costs them no more than $20 of real labour and parts to fix it, they should recoup the cost once the customer buys another two games and then be profitable again on all future games. Otherwise, if the customer doesn't buy another PS3* to replace it, then lost sales > repair cost and Sony loses. It would probably work even better if they charged cost price - few could object to a $20 charge for out-of-warranty.

*I never did understand why people bought 2 or 3 PS2s or X360s after successiev failures. You're giving the company incentive to make faulty products.