You used the bag, and in use a part broke.

It seems to me the request to send the strap for a replacement is a reasonable one, from the standpoint of a manufacturer standing behind its product (like a warranty repair).

It is unfortunate this can't be done in one day, but that is similar to any repair done under warranty.

I can see why the retailer wouldn't give you a strap off another bag from that or another store - that bag then becomes unsellable. The onus should be on the manufacturer to repair or replace it, IMO.