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).