We did eat swans -- at least in medieval Europe. Here's a recipe that involves coating the bird with lard and roasting it, then serving it with a sauce of giblets, blood, ginger, and galangal galingale.

In medieval England, swan ownership became highly regulated:

It appears to have been given Royal status in the 12th century, and thereafter, if a privately owned swan escaped, it became the property of the crown. By 1378 the office of 'Keeper of the King's Swans' was in existence and in a document entitled "The Lawes, Orders and Customs for Swans", dated 1482/3, the first law states that all swans owned by those who pay less than 5 marks a year Freehold were forefeit to the King. To own swans was, therefore, a status symbol and also provided a tasty ceremonial dish until superseded by the turkey early this century. It is recorded that in 1874, Prince Leopold, Queen Victoria's youngest son, sent one to his Oxford tutor, Dr. Ackland, for his family's Christmas dinner.

Privately owned swans bore intricate carvings on their bills, a little like a rancher's brand, which were registered with the royal swan master. (The tradition of "swan upping" still continues today, though the focus is now on conservation.)

The turkey arrived in Europe during the 16th century, where it rapidly replaced swan, peacock, crane, and other large birds served at banquets due to being much tastier. For ordinary people in England, goose would be the cheaper alternative for a very long time.