Hallo Erik,

tell me one, which is linear, means, is not demodulating in the GHz range.
An instrumentation amplifier, just the very high amplifying ones have a rather poor bandwidth. They can never handle cellphone radiation frequency. So, at this high frequency 'TRUE differential input' does not exist. The only effect is a demodulation (loss of linear characteristic) and produce of very strange, big offset voltages at output of instrumenation amlifier.
Make a test by yourself: Put cellphone close to any hifi-electronics , if there is no proper shielding or filtering you will always hear those 'pulsatings'.

The advantage of 'sqirrel cage' is that you can use ultra fast electrons in metal with their picosecond range reaction time to achieve extremly efficient shielding, just by a simple sheet of metal. Faraday cage is the only cure against NEMP (nuclear electro-magnetic pulse) and the only cure against lightning. Think of the man sitting in it's Faraday cage not becoming hurted, when 100 thousands of volts are sent to him.

That fact that an instrumenation amplifier looses all it's common mode recjetion ratio at cellphone frequencies has consequences on topology of filtering. Only capacitors at input routing interference to ground will help, not any capacitance between inputs. Only a common mode filter can help here.

There is some other fact, that highly recommends extense use of those 'quirrel cages': In the GHz range, phrases like 'electronic part', 'inductivity', 'resistor', 'capacitance' etc. looses it's meaning. At such high frequencies every piece of wire or copper trace is no longer 'some connection', but becomes something being 'active' in terms of radiation. They function like antennas. It's no longer electrostatics or eletromagnetics governing the behaviour, but electrodynamics.
And using Faraday cage is the best way to protect an electronic circuit 'clean' against cellphone radiation.

Bye,
Kai