What's your basis for concluding that verbal-reasoning ability is an important component of mathematical ability—particularly important in more theoretical areas of math?

The research that I recall showed little influence of verbal reasoning on high-level math ability, verbal ability certainly being correlated with math ability but the correlation almost entirely accounted for by g (or R). There's some evidence that spatio-visual ability, rather unimportant for mathematical literacy (as measured by SAT-M, GRE-Q), becomes significant at higher levels of achievement. But from what I've seen, the factor that emerged most distinctive for excellent mathematicians (distinguishing them from other fields also demanding high g) isn't g itself, but rather cognitive speed. Talented mathematicians are mentally quick.