Newer stuff is more efficient. For example washers and dryers have a direct drive technology with gears that help it use less power and maybe even less water.
FWIW, the same applies to most building replacements. Yes, the newer buildings use less energy, but the savings doesn't pay for the cost of replacing an old one.
That's never going to pay off in the long run. They're not significantly more efficient and they're less repairable, so the penny you save per wash is going to be more than offset by buying a new washing machine every five years when the bearing fails just out warranty.
New washing machines have a plastic outer drum that's welded together, so you can't get them apart to replace the bearing when it fails. They are designed that way so they're essentially disposable - after 5000 washes, you must replace the whole washing machine instead of a five quid part you can get from the tractor supply place down the road.
1. https://slatestarcodex.com/2015/05/11/california-water-you-d...
However ... when you move from the biggest picture view (in this case either state or regional water use patterns) and instead focus on a smaller, local one (e.g. the well(s) that tap into a single aquifer for all the 250 people who live here), a different story emerges.
The story: the low-water appliances may make no difference at the state/regional level, but they may keep our aquifer within its normal range during a 23 year and counting drought. That is, while our residential water usage is swamped by the ranches down the road growing alfalfa for their animals, it is still relevant to the state of our aquifer, and reducing that usage by 30-50% (as has been the case over the last 30 years or so) may play a significant role in not overdrawing the aquifer.