I haven’t read HP:MoR, so don’t know exactly what is happening in the example, but might you not have doubt about whether the supposition is false or not? Envisaging a solution is a way of interrogating the structure of the problem, including whether it is solvable at all. Sure though, if you want to use the suppostion to prove something else, rather than work backwards from it, you want to be sure of the supposition in the first place.
I haven’t read HP:MoR, so don’t know exactly what is happening in the example, but might you not have doubt about whether the supposition is false or not? Envisaging a solution is a way of interrogating the structure of the problem, including whether it is solvable at all. Sure though, if you want to use the suppostion to prove something else, rather than work backwards from it, you want to be sure of the supposition in the first place.