I agree, but plumbing and electrical codes can have specific things that are allowed or disallowed, and that can vary from place to place. One problem might be that to work on the washer, you would turn off water to your fridge, so you'd have to vent the lines after you turn the water back on.

For instance, a common kit in home stores is a thing with a valve that pierces a supply line, then has a coiled hose you connect to your refrigerator. I was watching an Ask This Old House video on this, where they said this was actually against code in all fifty states, because of the chance of a leak, but it didn't stop retailers from selling the kits.