I think the fact that Tim’s childhood was actually fairly normal makes things funnier, actually.
He was raised in boarding schools and a bit of a latchkey kid, but he knew his parents loved him and he was supervised the majority of the year. He has normal interests, like skateboarding and superheroes. He has plenty of friends and meets up with them outside of school and everything. Even when he has to go to a new school, he finds a friend group. He dislikes school and he’s a dork. He has had multiple girlfriends, a homoerotic friendship, and a boyfriend. He’s intended to be the reader-insert, the Everyman, the guy that teenage boy readers identify with. As far as Batman comics go, he’s practically Normal McNormal Face on a surface level.
Responds to a temporary lack of adult supervision by stalking Batman with a camera to prove that Batman is being reckless. How did Tim know Batman was being reckless in the first place? Who knows! Maybe he just stalked him recreationally first.
Travels to New York City alone to break into Dick Grayson’s apartment.
Tries to clone his dead best friend (the other half of said homoerotic friendship).
Climbs out the window in the middle of a conversation with his guidance counselor.
Fakes an entire uncle and hires an actor to play him because he wants to live independently.
Runs away to a quarantined disaster zone, resulting in a huge manhunt.
Deduces Batman’s identity at age 9 and keeps it a secret (look, 9-year-olds are chatty).
Falls asleep on a rollercoaster, in the middle of a stakeout, and other inopportune places like the freaking dormouse from Alice in Wonderland.
Desperately attempts to keep the family together in Gotham War to a frankly disturbing degree.
Routinely ends up in random countries without adults, but it’s fine because he’s Competent (TM).
Hero worships Dick Grayson so hard he literally steals his identity.
Like, no, Tim’s insanity is not the result of cartoonish childhood neglect. Which means…