in neither improv mysteries nor in Brindlewood do you, the player, solve a mystery.
That's not quite right. In improv mysteries you can have twists (which is encouraged), and the players can indeed solve the mystery. The GM ensures that a solution is possible, and the players solve it. It's possible to be wrong while the mystery remains unsolved and they still need to ask the right questions, plus the players are likely to come up with twists themselves. There's also the matter of what it costs to solve. The GM can keep it unsolved until a resolution would be satisfying, or they've ruled out other possibilities. You could run it as you describe, but it supports actual mystery solving by the players too. My characterization may have been harsh, but there's also room for both approaches as you said.