It may surprise you to learn that it doesn't! The practice of placing a vertical line midway across the postcard and using all the space to the right for the outbound address is a holdover from postcard designs dating back to 1907.
The term for the part of the postcard containing the outbound address is the address block, and the amount of space required for it depends on the elements of the address - the number of lines and the length of the longest line. In addition, the United Staes Postal Service (USPS) has requirements for the location of the address block and the barcode in order to qualify for postage discounts. But meeting these requirements generally does not require devoting the entire right half of the postcard to the address.
Depending on the size of the postcard, the amount of information in the address block, and other items such as the return address and the postal indicia, it may be possible to devote much more room than you thought to the sales message or teaser copy.