I think that's a serious misreading.Fantasy literature also predisposes to "rootless wanderers". Bilbo and Frodo didn't have much connections. They had a few bonds to others, but they were pretty weak.
The Hobbit is fairly light as a story, but one aspect of the humour is that Bilbo is so relcutant to go adventuring because of his roots - his home, his respectability, his connections to The Shire. The main reason he heads off is because of his friendship with Gandalf.
As befits a book that is more serious in tone, Frodo's roots are explored more than are Bilbo's. As well as his friendship with Gandalf, these also include his connection to his uncle, his friendships with Merry and Pippin and his connection to Sam (a romanticised conception of upstairs/downstairs,cross-class relationships). At the end of the story he leaves Middle Earth, but this is not a small thing. It's a great cost, as well as a reward, precisely because it means severing connections to places and people that were, and still are, dear to him.
If you look at the other hobbits, you see Merry and Pippin have their friendship with one another, their deep connections to the shire (as the future Masters of Buckland of the Smials, respectively) as well as the connections they develop to Rohan and Gondor. And Sam is so connected to the Shire that his conception of a reward is the magical soil and seed to make it floursih again, his conception of power being to spread the "green and pleasant land" of the Shire to the rest of Middle Earth. That's not a rootless vagabond.
Of other characters in the LotR, Aragorn's background drives a good part of the action, Boromir and Faramir both have very strong ties of family and loyalty, likewise Eomer, Eowyn and Theoden, likewise Gimli. Legolas's roots explain his presence in the action, but otherwise play a lesser role in driving his character - of the Fellowship, he is the closest to a rootless vagabond.
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