You overhype.

Everyone involved has to be sure what is being asked for and what progress has been made so far.

Not everyone, there is no obligation to be sure, and knowing anything with certainty is a questionable standard.

But to measure progress one needs to know what constitutes progress.

Not always. You can use your intuitions without understanding them. It helps of course, but not a requirement.

But to approach a solution, first and foremost, one needs to formalize the problem

Not at all first and foremost. Lots of problems have been solved without having been formalized. Again, it obviously often helps, but not a requirement.

which in turn means to be highly specific about what would constitute a solution.

Not "highly". If you are starting to work on the mystery of fire, you should refer to it as "That orangey-bright hot stuff over there," and not "An alchemical transmutation of substances which releases phlogiston." (although that would possibly be a different error).

And only by being strictly technical and by constantly trying to reduce any vagueness one can effectively approach the formalization of a problem and its eventual solution.

Again, false.