I think that the "send gifts to the bride's parents' home" likely originated during the era when it was uncommon for middle-to-upper-class women to work outside the home - therefore, the bride or her mother would likely be there during the day to accept deliveries.
And if they weren't, the maid was!
Or it was safe to leave them on the front porch or the mailman opened the door and set them inside the house.
Also, many, if not most, young women still lived at home until they married. So did many young men.