If you have collective washing machines as a public service running 24/7, the tradeoff may be worth it, but as a general rule it's certainly not the case. Extracting and refining materials for industrial processes consumes millions and millions of m³ of water and a lot of energy.

Our perception as consumers is skewed because the price we pay for electricity/water makes it economically more affordable to us to get newer devices, but from a resource usage perspective, that's certainly not a good deal for the planet. If we paid water/electricity the price that big industries do, we wouldn't even think getting a new device was a reasonable choice.