Collapse theories, in contrast, state that at specific points in time (the "measurements"), the wave function stops following the Schrödinger equation, and instead collapses to a single slice/branch/world, thus upending the natural proliferation of branches implied by the normal time-evolution of the wave function according to the Schrödinger equation.
Even in many-worlds, however, the wave function doesn't necessarily contain all conceivable worlds. It only contains the worlds, following from some initial quantum state, that follow from the Schrödinger equation. While it's true that all possible outcomes of a quantum measurement become real (because they are all contained in the wave function in superposition), "possible" here means specifically what the equations allow, not any imaginable world.