I'm sorry, but I don't see this working for complete strangers. It's true that extended families regularly exchange clothes, but they're not the real competition.
Your real competitors are the (fairly regular around here) mom swap events. You can buy the same quantity of clothes for less than your monthly charges and see what you're getting in person.
I have to agree with the second point. Lots of churches and other organizations hold fairly regular kids resale events in our area. They tend to be a step up from what you'd find at the thrift store, but they're still sold for thrift-store prices.
Not only that, but it sounds like what you get is sort of a "surprise bag" of clothes that you don't get to select. So it's sort of like Netflix, if Netflix just picked out movies it thought you'd like, rather than letting you select the titles yourself.
In that sense, the swap sales have a clear advantage. You see something you like, you examine it right there, and you don't have to buy anything you don't like.
Personally, I wouldn't use this service because it sounds like what's being offered are designer clothes, and that doesn't fit our budget.
What I'd love to see is a service that offers something like Finland's famed "baby box" -- which is given to all new parents:
It's got a bunch of basic outfits -- no frills, just simple, normal-looking clothes.
If a company were to buy stuff like this in bulk, it could probably put together a great, low-price, one-stop-shop "baby box" here in the U.S. and still make a decent profit.
Your real competitors are the (fairly regular around here) mom swap events. You can buy the same quantity of clothes for less than your monthly charges and see what you're getting in person.