OK, I'll weigh in:
Peak fitting is often useful in a situation where the physical structure is known only partially. If some feature of the spectrum changes in response to changes in some extrinsic parameter (polarization, temperature, or some such) then peak fitting can be a good way to quantify that response.
I think that PCA is a better way of quantifying the change with respect to an independent variable. For one thing, it tells you whether you can describe the change as a shift between two end-members, as in the reduction example, or whether you would need something more complicated. The obvious 'more complicated' is a combination of more species, for instance an initial form, a final species, and an intermediate for a reaction. However, another possibility, depending on the system, is some continous change in the structure, for instance, a bond angle which moves, so that one always has a single species, but that species changes. That could look enough like a combination to fool you. I don't know how to distinguish this sort of thing from a variable combination without knowing the science behind the system. For polarization, symmetry arguments would tell you that the data should be describable as a combination of two or three contributions, depending on what angle is being varied and what the symmetry of the system is. mam