It's unlikely we'll have our own warehouses, printing, and shipping infrastructure any time soon (if at all). I'm definitely open to working with a third party though, so facilitate sending the purchase information and relevant files off to be shipped. If you know of any services like that please share. Thanks for your feedback.
Yes all of that would be lovely, but
What I mean is the ability for me to keep stock at my home, take orders for them on itch, and then ship them myself. I'm just asking that itch could be a portal for handling that information - tagging a sale as a physical item sale, giving me the purchaser's address, and prompting me to ship product to them.
Ingram Spark has a company called Lightning Source that I am pretty sure has a backend API to do this. Another site uses it to fuel their print on demand program. I have no clue if it is an exclusive agreement, but it's worth checking out. Another company that might be able to provide this is http://www.chicagopressmen.com/ but I am not sure.
Warehousing wouldn't be the right way to proceed. Instead a partnership with someone that does print on demand would be appropriate -- a place that does just-in-time printing and shipping.
DriveThruRPG basically subcontracts Print On Demand stuff to LightningSource. I don't know all the details of that, but when a customer puts in an order, LightningSource prints and ships and individual copy for them, so there's no warehousing per se.
But as others have said, being able to set an inventory on itch and ship out books myself--like I do with my zines on Etsy--would be nice too. One of the big things with DTRPG is that I can let people order a POD book and get an electronic version for free at the same time (or set a discounted price to get both, but I just make the PDF free with a POD purchase), and it would be nice to have an automated way to offer that kind of combo through itch.