Intuitively, why is windowing function a low-pass filter?
Windowing is not a filter.

Windowing is a multiplication of two signals in time (the input samples with the window function: $x_w[n] = x[n] \times w[n]$ ).

What you get in the frequency domain is a (circular) convolution of the transforms of your signal and the window.

This convolution in the frequency domain can be seen as the spectrum being low-pass-filtered, giving a resulting spectrum with less detail.

[In the case of a filter, you get convolution in time and product in frequency.]