I suspect that the evolutionary reason is rather mundane; introspection (thinking about thinking and feeling) is expensive, and while it may confer some small epistemic benefit toward constructing and maintaining a theory of mind, the main benefit is in masking the downsides of other traits (like neuroticism, depression, anxiety, paranoia), which, to be frank, don't usually have much in the way of an upside. Historically (and likely prehistorically) it is simpler on a population basis to select against the traits that introspection would mask, which leaves introspectiveness as a trait that isn't strongly selected for, and at least slightly selected against in most situations.

This calculation flips in any situation where neuroticism, paranoia, etc. confer an advantage, which probably happens often enough to keep those traits (and introspectiveness) from dying out, and of course much of the stress of modern living exacerbates any neurotic etc. tendencies, which may give introspectiveness a boost even as those tendencies are selected against more strongly. But on an evolutionary timescale, I'd place a bigger bet on human culture(s) becoming less stressful, rather than on people evolving to better withstand stress.

Much of this speculation, TBH, is a handwavy just-so story. And since a theory isn't much use unless it has predictive power, here is a prediction: low-trust societies are where you would expect to find some minor advantage to neuroticism associated traits and a corresponding greater advantage to an even marginally better theory of mind, so we might find a correlation to greater introspectiveness. I am not aware of any research that addresses that question (although on an individual basis, neuroticism is by definition negatively correlated with trust, since trust is a facet of agreeableness)