Note that the equivalent circuit is an impedance divider:
The source is E-field around the probed trace. Likely quite a high impedance (an equivalent capacitance or whatever).
This drops into the probe's internal impedance (coil reactance, TL resistance, whichever). The drop across this element is what's sensed as CM-DM conversion.
Finally, the CM cable impedance (via shield exterior) sinks the CM current to ground or surroundings.
So it's an equivalent of three series impedances, the voltage drop of the middle one being what's measured by the instrument.
We can add ferrite beads to the cable to increase that last impedance, but notice this will only appreciably reduce the current injected by the source, when its impedance is comparable to the source impedance. So, if that's some kohms say (10kohm is a whopping 0.16pF at 100MHz -- probably typical for a probe right up on a trace), then we need at least as much ferrite bead impedance to reduce the error. Which is far from practical by ferrite bead alone.
Which is why these things are usually shielded, and balanced to whatever degree they can be (given that the probe's shield/housing will also be ground for convenience).
Honestly, I don't even mind the E-field sensitivity of the stupid little loop I made years ago:
(Notice it's two turns bare unshielded, one side grounded, so it's more directly susceptible than most proper designs.) I find it's not hard to separate E- and H-oriented components from the waveform, and can use the E-component to follow signals perhaps better than a well shielded one would. Downside, it's harder to get clean waveforms from, of course. But it's not like it's calibrated, it's only ever qualitative in use, and for that, just looking at the waveforms, relative amplitude, ringing, spikes, all of that, is perfectly usable. YMMV.
Tim