The United States Postal Service, or USPS, was founded in 1775 as a division of the government, which means USPS has the right to make legal restrictions.
According to postal regulations, no flyer or anything else mailable can be be put in a mailbox without proper postage.
Even if you put a stamp on your flyer, it is still illegal to put the flyer in a mailbox unless it was mailed through the post office.
It is also illegal to affix flyers, stickers, or anything else to a United States Postal Service collection box.
The only exception to the rule is a mail slot on a door or building. USPS regulations don't cover this, so you can insert a flyer into a mail slot.
- Image by Flickr.com, courtesy of Ed Siasoco