In physics, chemistry, materials science, etc. quantitative is orders of magnitude better than qualitative. In the social sciences the two may be the same quality but that's largely because they've had such little success with quantitative methods.
Quantitative is just a style of argument, and it alone can be used to argue for or against good or bad science. E.g. at the onset the Copernican Revolution, quantitative arguments actually were stronger for the Ptolemaic model. The core body of science, however, is a complex of evidence-gathering, hypothesis generation, and hypothesis testing, that collectively generate new sources of and frames for evidence. There's no particular reason that you've got to be able to build an isomorphism between a class of evidence and a numeric type in order for that evidence to be valuable and scientific.
On the other hand, I find it hard to argue with the observation that doing science with numbers seems to lead to a better and healthier scientific community (better in the sense of making testable predictions that pass their tests and suggest new lines of evidence).
> There's no particular reason that you've got to be able to build an isomorphism between a class of evidence and a numeric type in order for that evidence to be valuable and scientific.
As you hinted at, the experiment has been unofficially done many times and the evidence suggests the quantitative approach is better. That is the particular reason as far as I can tell. (Numbers may not be technically essential, but measurement and comparison are. That leads to things like everybody agreeing that a piece of metal in Europe is exactly one kilogram and everybody talks about mass in reference to that one object. It was a qualitative decision to choose which kilogram became the standard, but from then on measuring mass was quantitative and easily communicable. Fields that can't establish conventions for their observables in this way are generally not very scientific.)
My argument was that when holding the field constant puts qualitative and quantitative science on the same footing, it's a bad sign for that field. Take chemistry: when qualitative arguments were equal to quantitative it was called Alchemy. When quantitative approaches took over it changed the world.