Well obviously measuring anything high-speed requires the correct gear and know-how to use it. Just probing willy nilly with a x10 probe with a long ground lead mostly gives the same EMI ringing patterns on the scope screen even if you probed your ground plane against the same plane...
But gate shouldn't be that difficult, it's a fairly low-impedance signal (some ohms) with a lot of voltage swing where small fractions of volts are meaningless, you want to know if the gate is at 2V or at 4V at a certain point of time but quite some noise can be accepted in the measurement. Yes, high side has some fast common mode.
Measuring gate voltage is quite easy for the gate driver IC manufacturer with good enough accuracy if they think it gives some benefit to their gate driver operation.
"Kelvin sensing" the source terminal, drain terminal, and switch node is completely possible. The driver IC already has to include the floating driver, the same part can implement floating measurement.
OTOH current shunts are usually chosen to be small enough not to cause serious undesired Vgs negative feedback mechanism, saving the pins and IC design required for Kelvin gate driving. Minimizing the burden voltage is also desirable for efficiency and saving in power dissipation. For example my designs tend to have some 50-100mV max drop under max load and amplifier with some 50x gain. Such low burden voltage can be ignored in gate drive voltage discussion easily.
For really high frequency stuff Kelvin connections are required though to bypass source inductance which otherwise slows down switching.
Again, I'm asking what's the practical point of this discussion, have you seen a design which measures gate current, or have you seen some discussion about it? I.e., what point you are "hiding"?
And are you primarily talking about measurement on the lab table or in-application? Even that isn't clear to me yet, but the difference is huge; for lab, you can just buy decent gear (asuming it's not a shoestring budget hobby thing) and be done with it. In a design, you basically need the IC manufacturers to recognize nont only the brilliance but the real-world benefits of the idea of measuring gate current.