That seems like a really precarious position for those startups to be in. First there's quality-control: the #1 thing that's going to wreck your relationship with a laundry customer is if you mess up their clothes, and if all the clothes-handling is outsourced, how much can you do to prevent that from happening?
And second, if all the value you bring to the table is a thin layer of code over someone else's service, at some point that someone else will just write their own app and cut out the middleman. "Climbing the value chain," the MBAs call it -- start off as a provider of outsourced services to companies whose executives' noses are too high in the air to do their dirty work themselves anymore, and then slowly shoulder those companies out of the way by establishing direct relationships with their customers at a lower cost. It's a strategy Asian hardware OEMs have been pursuing with success for decades -- there's no shortage of people who used to be IBM and Dell customers who are Lenovo and Asus customers now.