On the other side of the coin, if the head fails out of warranty, then you've probably just justified the expense (although Canon seems to be 'not terrible' about some leeway on this).
Yes, but the key word here is "probably", behind which lies the whole story of risk, insurance and warranties. An extended warranty is an insurance policy. If the people designing it do so based on principles of insurance, we can assume it is not their intention to lose money on this business. So when they price this warranty, somehow they will have made projections of how many such warranties they will sell, how much total income that will bring in to the business, and how much is likely to be expended on claims. To do this, they will always have more information than consumers about what is likely to be needing replacement or repairing over the period of the warranty, with what probabilities of occurrence at what costs to the company, plus admin costs, and therefore how much will be their aggregate layouts. They would be looking at aggregate layout relative to aggregate income and aiming for at worst a balance, and at best a positive return. For individual consumers the equation will always be <Risk = Probability of Occurrence x Value of Consequences>. Consumers don't have the data to evaluate the Risk, so cannot make a rational decision about the financial prudence of buying the warranty.
Peace of mind isn't a consideration insofar as once you've bought the warranty you may be anxious over the whole period about whether it was ever necessary, and if you haven't bought it, whether something will happen to the printer over the same period making you regret that decision. I think the peace of mind business is awash. One thing I do know for sure, however, is that if I spend the $650 on the warranty, there is a 100% probability that I am $650 poorer than I was before, whereas if I don't spend it, there is X% probability that I COULD be $Y100 worse off at some time in the future. What are the values of X and Y? We don't know.
Taking this down to the level of practical reality, let's say head replacement is the most probable risk. As a consumer beyond year 1, if nothing else but the head goes wrong, the value of the warranty is Prob(head replacement) x Cost(head replacement). The price of the head is USD 675. The probability of replacement within that warranty period is let's say 20% (this is hypothetical, I have no idea). In principle, the value of the warranty would then be 0.2 * 675 or $135, for which the customer will have paid $650. If the customer falls into the 0.2 population, the net benefit will be $675 minus what was prepaid for the the warranty, or $25. If the customer falls into the 0.8 population, he loses $650. Is it worth it? Do we have enough information about this model to begin to know?