Yeah, there's nothing that would stop you from having a process where, effectively, the PCs construct the mystery as they go and create the solution. It might not be satisfactory to some people, but if the point is to explore the process rather than the mystery itself, its still valid.
So, let me talk about the Fate-based Atomic Robo RPG for a moment.
There isn't a whole lot of light between "solve a mystery" and "solve a science-fiction problem". Characters have to gather information, come to conclusions, realize what's up, and give some pseudoscientific gobbledigook about a solution and roll dice.
In Atomic Robo, they lift the burden of what is actually happening from the GM. The GM says that humongous, building sized ants are rampaging towards Las Vegas! What will we do??!? The GM does not have to know how humongous, building-sized ants work, or what their vulnerabilities are, or lay clues as to how the humongous ants can be defeated. There is, instead, a brainstorming mechanic, in which the sciencey characters get their heads together, spitball some ideas, build on each other's ideas, and come up with a helpful result (in Fate terms, they produce a known Aspect of the thing in question that can be tagged for bonuses).
This works for what it does, because we can be honest and note that even if the GM has a doctorate in entomology, they are going to get something wrong - they have to, because real ants can't get that big for real reasons. The ants are fundamentally inconsistent with the real world, so someone is going to have to wave their hands and excitedly say, "But quantum mechanics!" or something to make it work. Might as well let the players do that bit, right?
One imagines we could transfer this to mystery solution, but it fundamentally fails on two counts:
1) In super-science nonsense, you do get to wave your hands and excitedly say, "But quantum mechanics!" to cover for any inconsistencies. Satisfying mysteries need internal consistency.
2) Mysteries, as a genre, are about being clever - both the author and the audience. Just making it all up at the end does not scratch the itch of actually being clever for the GM or the players.