Digital filtering based on frequency component amplitude... why not?
I can tell you why I avoid such methods. When you pick some frequencies above threshold and remove others, you are using a kind of hard limit. In DSP this is same as Rectangular Windowing in frequency domain. It's effect in time domain will cause ringing. Because when you multiple in frequency domain with rectangular window, in time domain the signal gets convolved with a sinc function. There is a whole wikipedia page dedicated to this (Gibbs Phenomenon) - https://en.wikipedia.org/wiki/Gibbs_phenomenon

Again it depends on our requirements though. For example, if you see your filtered signal, the rise and fall time are not steep compared to original signal because you have eliminated higher frequencies which contribute to this. If my requirement was to apply a filter without compromising on fast rise time, I would not choose this method.