Some years ago, I actually had to learn about this. There are adhesives that are flexible, strong, hypoallergenic, and can survive laundering. They're used for disposable diapers, automotive applications, gloves, purses, luggage, and such. In a production environment they're applied as hot sprays, which requires compressed air and heated hoses and tanks.

Sewing isn't expensive, though. It costs more to get the fabric lined up properly for sewing (because that's manual) than to sew the seam.

(Former member, American Laundry and Dry-Cleaning Association.)