The Anime Lad
Tsunayoshi Sawada is unpopular, unsuccessful at school, and generally regarded as incapable. Then Reborn arrives. The professional hitman has been assigned to train Tsuna as a future boss of the powerful Vongola family. Tsuna lacks confidence and relevant experience. The succession process proceeds anyway, suggesting organized crime has adopted developmental hiring.
Super Eyepatch Fox
Tsuna cannot manage middle school. The Vongola family expects him to manage organized crime. Reborn arrives as his personal hitman tutor and begins training immediately. Face ordinary school problems under extraordinary pressure. Survive the lessons. Handle a career path nobody asked Tsuna to choose.
Gigguku
Tsuna is spectacularly unqualified for daily life, so naturally a professional hitman appears and announces that he will train him to lead the Vongola family. WHAT a promotion! Ordinary middle-school problems now sit beside mafia expectations, and Tsuna's panic is completely reasonable even when the premise refuses to acknowledge it.
Father's Basement
The setup depends heavily on humiliating an unpopular middle-schooler, and Tsuna's helplessness can test patience immediately. Reborn supplies the necessary pressure. He treats an ordinary student's problems as preparation for organized-crime leadership, while Tsuna has no qualifications or desire for the role. The absurd mismatch is the cleanest reason to watch.