Interesting observation ! Might it be because Tesco and Costa resemble ordinary names, and therefore easily appear in a possessive form ?
Or it might be about imaginary hierarchy. There could only be one actual duly-anointed king of burgers, but if one were to use the definite article to mark this, saying "I am going to the Burger King's", it would imply firstly that the king of burgers does actually exist, and possibly also secondly that he has but one solitary burger outlet.
A grammatical construction not quite so jarring when used with (say) "Tesco".
Or it might be about imaginary hierarchy. There could only be one actual duly-anointed king of burgers, but if one were to use the definite article to mark this, saying "I am going to the Burger King's", it would imply firstly that the king of burgers does actually exist, and possibly also secondly that he has but one solitary burger outlet.
A grammatical construction not quite so jarring when used with (say) "Tesco".