I do interpret the question "why is windowing function a low-pass filter?" in another direction: why can a (typical) window function be interpreted as the series of coefficients of a low-pass filter? Because of the duality between the time and the frequency domains, so:
Mostly because the coefficients of a normalized window sum to one (which could not be said, for instance, about most wavelets, which are zero-sum)
Most classical windows are positive, symmetric, and can be normalized so that their samples $h_i $ sum to one (since $\sum_i h_i \neq 0$). Their coefficients can be interpreted as weights, and you can replace a signal sample by a weighted sum of other samples and the window weights: each weighted one is replaced by a center of mass. It suffices to divide the result by the sum of weights to get an averaging filter (center of gravity). Since most standard windows are symmetric and often unimodal with maxima at their center, they look like regular smoothing filters: a rectangular window convolves like a moving average filter, a Bartlett filter, a Gaussian window ... like a Gaussian filter.
So, smoothing with a box or a triangle somehow boils down to interpreting a windowing function as a low-pass filter.
Moreover, a repeated (or parallel) use of box rectangular windows of different sizes is used to approximate more complex filters, in a very fast fashion, see for instance Theoretical Foundations of Gaussian. Convolution by Extended Box Filtering, 2011.