My parents (suburban middle class family) still use the service to this day.
How do they justify it? The milk is better quality then anything that's mass produced in the grocery store (and my parents still go to the grocery store regularly) and doesn't contain all of the growth hormones. I would argue it is very niche though.
No one is going to argue that this is cheaper than doing your laundry at home. The simple fact is: people pay a premium for convenience. You should be comparing Prim's pricing with other laundry delivery services not the cost of doing laundry at home. Many laundromats deliver for free and charge between $1-1.25 per pound. If you figure that 20 lbs of laundry fits into a standard laundry bag, then Prim's per pound rate is $1.25; on par with many laundromats offering "free" delivery and pick up. Now, assuming you send your laundry out already, and Prim is offering a superior service (better customer service, an easy to manage online UI, etc) than other laundromats, selecting them as your provider is a no brainer.
*Disclaimer: I've been working on the same model as Prim for a few months and will be launching in a major city in the next few months. The economics are there, even on a small scale. Scaling up is where things get really interesting.