I purpose instead that the reader should identify Frodo and Sam as occupying a shared responsibility as the figure of the Maimed King in which Sam comes at the end of the story to occupy the role of the Maimed King Restored. Sam and Frodo are closely connected throughout the novel and the notion of a shared responsibility of the Maimed King would have been familiar to Tolkien, especially if, as Flieger suggests, his referenced source was Malory whose Morte d'Arthur features no less than four characters in the position of the Fisher King of which two are distinctly separate Maimed Kings. This also fits with Flieger's observation that Tolkien rarely ties his characters to their traditional source counterparts directly: "The information is given obliquely, however, for, as with Aragorn, Tolkien avoids a one-to-one correlation between Frodo and earlier medieval heroes" (Flieger, 137).
Think of it this way, Sam begins to attain Frodo's former status in the Shire. Beginning at the moment the Ring is destroyed (Tolkien's grand act of healing identified with a relic that is quested for) when Sam wakes up to Gandalf who addresses him as "Master Samwise" (Bk VI, Ch. 4). Sam has never been a Master of any sort, yet Gandalf and subsequently Galadriel (Bk VI, Ch. 9) refer to him as such after the destruction of the Ring of Power. It is Sam and not Frodo who is referenced as healing the Scoured Shire ("Meanwhile the labour of repair went on apace, and Sam was kept very busy" Bk. 6, Ch. 9) and subsequently becomes Mayor. This act occurs almost in the same breath in which Frodo designates Sam as his heir and the reason he gives for Sam's qualifications as mayor are that "your hands and your wits will be needed everywhere" (Bk VI, Ch. 9). Samwise takes on the role of Maimed King Restored having fully replaced Frodo's former functions in the healed waste land. Not only that but Frodo draws clear associations between Sam as Mayor and Aragorn as Healing King both of whom have "healing hands" and act ultimately as gardeners.
Interestingly the question of heirs also acts to reinforce Frodo and Sam's shared role as the Maimed King. In traditional Arthurian accounts the Maimed King is often said to have suffered a wound to the thigh implying that the wound has made him impotent. Impotency is important in the symbolic role of the Maimed King since as he suffers so too does the land which fails to grow anew and suffers a similar lack of fertility. And while Frodo does not have any heirs and therefore designates Sam, Sam has a number of children by the end of the final book. Sam's potency in the land of the restored Shire serves to highlight by contrast Frodo's continued 'impotency'. In this way, we can read Sam's close relationship with his Master as having deeply significant ties to the dynamics Flieger highlights between Frodo and Aragorn, linking the character back to a deeper medieval tradition.
*Title is a reference to T.S. Eliot's "The Waste Land" a post-modern retelling of the Maimed King story