Square impulse stimulation.

[Raj]

I can see two reasons:

Sociologically:
Square pulses and ramps are among the most used signals experimentally. Neuroscientists are used to them and know how to read the results. So if you use square pulses often your discussions with others become a lot easier.

Experimentally:
Another reason is that introducing smoother stimulus forms will make the analysis of the dynamics more difficult because you mix the dynamics of your signal with the dynamics of the system under study. Creating a sudden change in for example membrane voltage allows you to look at the effect as completely due to the internal dynamics of the cell and thus allows you to extract information about for example rate constants at a fixed membrane voltage. The reason is then the limitation of the experiment you use for comparison with your model.

[ted]

Not to encourage or endorse religious debates about stimulus waveforms, I happen to
be an electrical engineer, and count many EEs among my friends and acquaintances.
I am unaware of any prejudice whatsoever, by anyone, against pulses of any shape.
Why, where would textbooks on linear circuit theory be without all those examples
that invoke rectangular waveforms? The sinusoid may dominate the frequency domain,
but the square pulse rules the time domain.

And, to strike a patriotic stance, where would this great country be, if it were not for
Samuel Morse's invention of the telegraph, an instrument whose very essence is the
rectangular pulse? I recall hearing somewhere a Russian claim to this invention, but
it couldn't get very far in that country because the cold winters would freeze the little
square waves to the wires until the spring thaw, when a veritable avalanche of dots
and dashes would crash down upon the telegraphers' huts along the Volga, often
with disastrous consequences.

But I digress.

The smearing and loss of amplitude of square waves coursing over long distances
was a serious problem for the practical application of telegraphy (to paraphrase
N.J. Baker, one of the truly great kineticists, "egg-shaped, or pear-shaped, all
waveforms lose their shape") . Another was the question of how to improve the rate
and quantity of data transfer along a pair of wires. These challenges led to theoretical
and practical advances that benefit neuroscience today: cable theory, information
theory, and technology for amplifying and preserving the shape of signal waveforms.

[Raj]

If we absolutely need to quote authorities lets quote one relevant to the subject area:

Step potential changes have a distinct advantage for measuring ionic current I_i since, except at the moment of transition from one level to another, the change of membrane potentia dE/dt, is zero. Thus with a step from one potential to another, capacity current I_C stops flowing as soon as the change of membrane potential has been completed and from then on the recorded current is only the ionic component I_i. Much of what we know today about ionic channels comes from studies of I_i.

To which I like to add that the ionic channels themselves behave rather nonlinear, which makes them less well suited for linear analysis through fourier methods. Mathematically the right tool to probe the transfer properties, with which I have no experience but know to exist, would be through characterizations using Volterra kernel methods or other kernel methods. For some of these kernel methods the most suitable source for probing the system is said to be noise or a (pseudo) random signal.

In Modern Techniques in Neuroscience Research, U. Windhorst and H. Johansson eds, you can find a introduction to the subject of nonlinear kernels in the chapter: Nonlinear Analysis of Neuronal Systems by Andrew S. French and Vasilis Z. Marmarelis.