DFT - Removing window effect in spectral domain with convolution
There is, in fact, a downside to your suggestion: the signals you showed are all very clearly divided into their frequency components, but in general, real-life signals tend to be more noisy. 

Depending on the application, you'd want as much leakage dampening (higher main lobes/smaller side lobes of a signal frequency in the transformed spectrum) or, as another example, the narrowest possible main lobe.

In your plots, it is visible that smoothing the magnitude spectra with a window does the opposite of these: the main lobes get wider and smaller, while leakage products from transforming a finite time signal gain in power. Applied to noisy signals, this would yield a significant disadvantage.

Your suggestion, however, is still pretty useful for peak identification!