https://users.pfw.edu/wootdm01/bilbo.html
Personally I think that as well as their local status, their class can also be analyzed from a global perspective, where the hierarchy of the wider world still goes Eru > Ainur > Maiar > Eldar/Edain / Other Men/Elves > maybe Dwarves > everything else including Hobbits. In global Arda it matters not that Frodo was amongst the wealthiest and highest-status Hobbits - they are viewed as marginal by the other races, and it was this very marginal status that caused the “higher” races to overlook their potential, which is a large part of how they succeeded.
I’ll also defend the idea that the military strategizing of Great Men was for nought. We are told quite clearly that the ring is the only hope for free peoples; that even if it is kept from Sauron, his forces will inevitably win. Aside from Aragorn and possibly Faramir, the ruling Men are depicted as weak and flawed. No, they’re not taken to task for this, and royal birthright prevails, but then Tolkien as a Catholic wasn’t aiming to demonstrate anything about class liberation - hence my reading of the story as being one of cross-class collaboration, and the wider point being that achieving meaningful change is likely to involve “big people” and “little people” finding ways of working together.
Prince Imrahil is also a great noble of Gondor. And in Rohan, we see Éomer and the late Theodred without notable flaws. Flawed but nonetheless worthy nobles include King Théóden, Lady Éowyn, and Boromir. Steward Denethor is a complex case. King Brand of Dale is largely outside of the story proper, but is also seen as a great leader.
The Marxist analysis seemed to me flawed, particularly in presenting dwarves as below men in the social hierarchy. The men of Laketown had an elected leader; the dwarves had a kingdom, and though driven out of it they had regained some measure of wealth in their lands of exile. They were indigent at Laketown, but that's because they'd lost much on their travels. Nonetheless, they were fêted. Once re-established, the kingdoms of Erebor and Dale were close allies, and dwarves and men lived in harmony.
I agree that ruling classes are not taken to task; in fact they are celebrated throughout the books. On the other hand, the wise and powerful rulers cannot win on their own. Only the secret mission of Sam and Frodo could achieve victory.