Almost any modern game you can name, button held down to go faster than the full tilt of the analog stick. Other hold function that might have been assigned therefore impossible. That button nearly always used for dodge, since full run is logical extension of dodge, but means every game is now way more about dodging and it's not enough to move around and position yourself well with the stick anymore. Attacks track you anyway, because they really want you to use that run button. Some of these games don't even let you jump, because RPG elements in everything means one of the other face buttons already dedicated to item pick up or use. Usually face button is run, meaning camera can't be as easily and comfortably manipulated. Additional features then need to be inserted to balance this full run: stamina, fog walls that keep you in the fight, stamina... But in nearly all of them player can still sprint past/around all the enemies, because run button is that OP.
Name 50 examples.
You could have just looked at your own library of modern third person games and tried to remember which of them let you fully run with just the stick. Almost none of them.
I will limit myself mostly to modern third person games with a run button. The rest of what I talked about varies. Will name button inputs even for games that play better with a KB/M for consistency.
Metal Gear Solid V
The Legend of Zelda: Breath of the Wild
The Legend of Zelda: Tears of the Kingdom
Batman: Arkham Asylum*
Batman: Arkham City*
Batman: Arkham Knight*
Batman: Arkham Origins*
Demon's Souls
Dark Souls
Dark Souls II
Bloodborne
Dark Souls III
Sekiro
Elden Ring
The Last of Us (button L2)
The Last of Us, Part II
Tomb Raider
Rise of the Tomb Raider
Shadow of the Tomb Raider
Returnal
Grand Theft Auto series*
Red Dead Redemption series*
Days Gone (L3)
God of War 2018 (L3)
God of War: Ragnarok
Marvel's Spider-Man
A Plague Tale
Astral Chain (L3)
Death Stranding
Callisto Protocol
Control
Echo (IIRC)
The Evil Within (L1)
Hellblade (L1 or L2)
Horizon: Zero Dawn (Come to think of it, L3 to sprint is likely mandated by Sony.)
Little Nightmares (left face button)
Mad Max (R2)
Max Payne 3 (I don't know which button it is. Only play this with KB/M.)
Metal Gear Rising (R1)
Middle-Earth: Shadow of Mordor
Middle-earth: Shadow of War
Nioh
Nioh 2 (Dodge and sprint on bottom face button.)
Quantum Break (L1)
Sable
Resident Evil 6 (But RE always had a run button.)
Sleeping Dogs
Sniper Elite (L3)
Spec Ops: The Line (Sprint button shared with cover and context sensitive actions. Can't remember what this mediocre game plays like, but this sounds gross.)
Star Wars Jedi: Fallen Order (L3)
Star Wars Jedi: Survivor
The Takeover and Fight'N Rage (Double-tap direction, like in River City Ransom and declined Streets of Rage 3.)
The Division (L3)
Watch Dogs (R2)
Vampyr (Right face button is dodge and sprint.)
Vanquish (IIRC)
The Witcher 3 (Hold bottom face button to sprint.)
Infamous: Second Son
Dragon's Dogma
Nier: Automata (Dodge button)
*Even worse because default movement is walk.