Grounded base operational amplifiers

In my wild thoughts, I had a wild idea. I am not at a stage of my life that I can follow through.
I am carrying ou some experiment related to Faraday disks. Faraday disk
provide low voltage at relatively high current. The input impedance of a typical voltmeter is too high to register the output voltage. It would be helpful to have a low impedance input ammeter for such measurements.
The usual way of handling this is to make a transimpedance amplifier our od an op-amp (operational amplifier). A feedback resistor from the output reduces the voltage at the input to the amplifier to turn it into a virtual ground. The signal would usually be applied to the base of a transistor with a grounded emitter.
It seems to me, that little actual current flows into the first stage of the amplifier under these circumstances. It just seems that noise can be reduced by taking advantage of the Faraday disk property that it can deliver large current. This makes me think that a grounded base transistor should be used. The input impedance at the emitter will be low so that many times more current will flow into the active device than if a conventional op-amp is used.
Somehow, I would think that if the circuitry does not have to "work hard" better performance can be achieved.
I have not thought this out. My summarizing question is: what are the relative advantages of high impedance common emitter input op-amps and common base input op-amps (whatever they are) as the source impedance varies from almost zero to almost infinity?
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