How does this concept affect the transimpedance phono amps?
The input impedance is also known as 'virtual ground'. This is a point in any opamp circuit where the feedback is applied back to the input of the opamp. There is a resistor that also connects to that point, which is the input resistor, in series with the signal. The ratio of input resistor vs the feedback resistor sets the gain of the circuit; if the feedback is 10K and the input resistor is 1K the circuit has a gain of 10.
In a transimpedance amplifier, the cartridge itself is that series input resistor. Part of the reason for doing this is to reduce noise, since the Johnson noise of the resistor itself contributes to the noise floor. You can see that the gain of the circuit varies according to the impedance of the cartridge winding; as the impedance of that is decreased, the gain of the circuit goes up. Even with modern opamps care should be taken to keep this initial gain less than 20dB else you can get into distortion issues.
What is important to understand here is that the cartridge isn't actually driving ground, which is what zero Ohms would normally be! Its driving the relatively high input impedance of the amp amp, and is also interacting with the feedback signal. However the cartridge is remote- it is likely feeding a tonearm cable a meter long or so, so the RFI generation will still be present. So loading might still be required.
If the voltage drops as the loading is applied i won’t be linear power.
Since the minimum load specified is 10X the source impedance, we're not talking about a big issue here.