Intuition behind using non-hypercubic kernels in density estimation
Histograms and methods based on binning have a number of well-known problems. Different anchor points etc. can introduce artificial patterns that make interpretation unreliable. Smooth kernels don't use a grid and thus smooth out the noise. 

This also has the advantage that it makes it easier to get a single overall picture of the data because it takes into account neighboring points and smooths the data into areas where no data is observed.

Smooth kernels can also be justified by their favorable statistical properties. Popular methods like fastKDE use the fact that one can find "an empirical kernel that is optimal in the sense that the integrated, squared difference between the resulting KDE and the true PDF is minimized."