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.