What is the need to do a dV/dI measurement instead of numerical differentiation?
Numerical differentiation of real data tends to cause noise problems. 

It's easiest to explain in terms of a time series. You know the Fourier transform rule for derivatives is 

$$\mathcal{F}\left(\frac{\mathrm{d}f(t)}{\mathrm{d}t}\right) = (j\omega)\mathcal{F}\left(f(t)\right)$$

where \$\mathcal{F}(\cdot)\$ is the Fourier transform operation.

This means the transform of the derivative has more energy at higher frequencies, compared to the origianal function. 

Usually, your signal is bandlimitted (or smooth), so that this doesn't cause the F.T. of the desired function to blow up. The problem is that real measurements have noise (or random errors), and almost always there is a noise component which is "white", meaning it has roughly equal energy at all frequencies. When you take the numerical derivative, you will also be taking the derivative of the white noise component. And the spectrum of the derivative of the white noise component will increase at high frequencies, often to the point that it swamps the desired signal.

To avoid this problem, you might try to smoothe or filter the data before differentiating. That will help, but the problem is still fundamentally there.

And although it's most obvious why this problem exists for time series data, the same math applies even if your data describes some other relationship like an I-V curve.

That said, I don't think it's uncommon to do differential resistance (\$\frac{\mathrm{d}V}{\mathrm{d}I}\$) measurements using numerical differentiation. If you were using a measurement system with low noise SMUs ilke an HP/Agilent/Keysight 4155 model, and use long enough integration time for each measurement point, you would likely be able to get adequate results for most purposes.