They (Merry and Pippin, the sons of the aristocratic Tooks and Brandybucks) actually rallied the poor farmers (e.g. the Gamgees and the Cottons) and the middle farmers (e.g. the Maggots) against the kulaks (whatshisface from the southfarthing and the Sackville-Baginses) backed by an invading industrial power (Saruman)
Any "coup" was really the traditional authorities being restored to power by a lower and middle peasant uprising bc it is a fairy tale written by a medievalist who wishes capitalism and industrialism never came about. Principally bc tolkien hated the destruction both have wrought on the natural world and on humans. (And to his credit, he was consistent enough in his hatred for modernity to oppose the whole british imperial project, despise the spread of the english language, refer to british soldiers as orcs, and in The Hobbit imply modern europeans are goblins.)
Idk what you mean by lynching, the book is very explicit that the only deaths were in the battle (+Grima and Saruman), that all who surrendered were let go and that Frodo is constantly trying to get the hobbits to be LESS violent
The Hobbits faded bc hobbits dont exist in 1900s and Tolkien is writing a fairy tale that takes place in the past. Also the "progressive" rule of Saruman was literally an ecocidal human supremacist dictatorship where the only growth industries were policing and exports to the imperial core down south (which, quite explicitly, does not happen under Aragorns kingdom)
Also to reply to your other comment here, the Gamgees arent "slaves", as Sam's father recalls (literally the first conversation in the book!) it is a job he got via family connections. In the Shire, gardening is skilled labour. Hamfast is literally called "Master Hamfast" by Bilbo and respected by all for his knowledge of gardening.
Lastly wrt your point about the aristocratic families having power, the books are actually quite explicit that those families have no real coercive power (the only military the shire has is the entire shire raised, there is no coercive apparatus separate from the whole people). In all but aesthetics (which, bc of the hobbit, are locked into a weird mix of neolithic britain and 1870s england), the hobbits are a tribal society only shortly removed from primitive communism / kinship economy