Player improvisation can happen no matter which paradigm the game is under. It's about level of scale and impact.
You mention the classic examples of flooding the dungeon, but I can counterpoint with a classic example of player improvisation in combat as sport: swinging on a chandelier across the room.
The difference is in scale. Combat as sport has small-scale combat options on the character sheet. War has macro-scale options on both the character sheet and in table-wide rules. Compare old Vancian-style casters who could delete an encounter with a Sleep spell, but the gameplay was about choosing when to do so. To something like 4e sorcerers who had buttons to press, and got the pleasure of dithering over encounter and at-wills every single fight.
War wizard decision is at the macro scale. Sport wizard decision is at the round during the encounter scale. Both can improvise, but usually tend to improvise at the scale they are expected to operate at.
Theater instead flips the focus and improvisation to the PC's story, and improvisation is therefore generally found there instead. Smoking out the dungeon would be considered a dick move for table vibes. Focusing too much on combat min-maxxing loops instead of flavor and shared spotlight likewise.