Why we can't use step function to identify system's transfer function
The conclusion of the author is incorrect. It is in fact possible to use step response data to measure a system's transfer function, it's just a bit more complicated. This is done all the time when evaluating time domain reflectometry and time domain transmission measurements.

The main issue is that the author defines a step to be "a sequence consisting entirely of 1's", which is not a universal definition. A step function should be 0 for t &lt; 0 and 1 for t > 0. For some reason the author of your web page seems to think t=0 is the beginning of time and there's no way we can get data for t&lt;0, which is not generally true.

However if you use a dataset where you start at some t0 &lt; 0, you will have to account for the delay factor when doing your data analysis to calculate the transfer function (if you care about getting the phase right).

Also, you will need to understand about applying a window function to your data before doing the numerical transform, because the common DFT (aka FFT) assumes a periodic signal. This means it thinks the sample after your final sample will be a repeat of your first sample, and so on. This will often cause there to be an artificial second step (with very high frequency content) at the boundary between the last and first samples. Applying a window function (for example a Hamming window) will minimize the effect of this discontinuity, but also introduce some "smearing" in the computed frequency-domain transfer function. See a textbook on DSP for further details on this issue.

Finally, you will, as alluded to in the web page, run into a problem at high frequencies. Since the power content of the stimulus signal is falling off like 1/f, eventually the response signal will be below the noise floor of the measurement system, and the measurement will not be meaningful. Said another way, when you compensate for the 1/f fall-off of the stimulus in calculating the transfer function, you will enhance the noise at high frequencies.