This is assuming it’s sealed and has a proper stamp. Post cards are more expensive than cheese. And who doesn’t like cheese right?
This would be prohibited by the USPS:
5 Perishable Matter
51 Definition
511 General Definitions
Perishable matter is anything that can deteriorate in the mail and thereby lose value, create a health hazard, or cause an obnoxious odor, nuisance, or disturbance, under ordinary mailing conditions. Mailable perishable matter may be sent at the mailer’s own risk when it is packaged as required and when it can be delivered within appropriate and reasonable time limits to prevent deterioration. Examples of perishable matter include mailable types of live animals, food items, and plants.
Full list of prohibited items
American cheese doesn’t look like it’ll ever deteriorate.
Does Kraft “cheese” really count as food though?