How would it work in practice? I could make any calculation come out however I wanted by simply declaring whatever arbitrary axioms were required to produce the result I wanted.
For instance, Einstein's special relativity is built on several postulates one of which is a four dimensional space/time continuum. Falsify that and the entire theory is falsifed.
Mathematics is formal and thus the presuppositions are known up front. In my view, scientific investigations should be formalized the same way.
Thus, if the scientist starts with a presupposition that the earth sits on the shell of a giant, invisible turtle, there's no need to read further except perhaps for amusement.