Let’s say you have a kitchen faucet with a high flow rate of 2 gallons per minute. And let’s imagine you need to run the sink for a long time, say a full minute. So perhaps you lose 2 gallons of cold water to flush the lines. (Assuming you don’t do anything with that water, which you can certainly choose to do so.) Some searching suggests the average cost of water in the US is $5-8 per 1000 gallons. Let’s make it a round $10 per 1000 gallons, or a penny per gallon.

So, even with generous assumptions, it costs you 2 cents in wasted cold water as you flush the lines every time you run the dishwasher. If you run the dishwasher every single day, that comes to $3.65 in wasted cold water. If the fancier dishwasher with the better heating element costs only a hundred dollars extra, it will still take 27 years for the extra cost to be paid back via saved water.

In practice, these numbers were chosen to be generous, and the payback period is likely over a century. Your dishwasher will not last 27 years, let alone a hundred. Plus the time value of money. In short, the fancier heating element will never come close to paying for itself. You’re paying for a convenience, not saving money.