The comparison people actually make, and why it misleads
The usual instinct is to compare a purchase price against a monthly fee, work out the crossover point, and treat that as the answer. It is a clean calculation and it leaves out most of what matters.
A purchase price is a known number. What follows it is not: maintenance, repairs, the timing of those repairs, the cost of being without ice while a repair happens, and the replacement decision at the end. Comparing a certain number against an uncertain stream and concluding the certain one is cheaper is not a comparison, it is a rounding error dressed as analysis.
The more useful framing is that these are two different structures for the same requirement. One concentrates cost and responsibility at the start and disperses it unpredictably afterwards. The other spreads it evenly and moves the responsibility elsewhere.
