@ElizaBennett - Until recently, I had no idea that diaper laundry service still existed! I don't think they're available in all areas.
Something you didn't mention was the possibility that a parent might want to cloth diaper, but not have their own laundry! In that case, a diaper service might not be exactly the *only* option, but it's certainly the most appealing!
My cousin got into cloth diapering by accident. Her son is very chemically sensitive and every brand they tried made him break out in a rash until finally the pediatrician suggested going with cloth.
But they don't have a washer and dryer. So they were very fortunate to be able to locate a diaper service that can do that job for them. They said the only downside is that they only have once a week pickup, so when you open that airtight container to put more diapers in, the smell is *incredible*! It's probably much less an issue if you wash more often.