While I understand your reservations, I think you are really underselling the power of Ansatz. Ansatz reduce the search space of possible solutions because it

While I understand your reservations, I think you are really underselling the power of Ansatz. Ansatz reduce the search space of possible solutions because it adds various constraints that makes it possible to get to solutions much faster. For example, without these constrained searches we will never have developed any analytical solutions to differential equations that are pervasive across science, engineering, finance among others.