If the resistance of a shunt resistor in a circuit is acceptable, is there benefit to any other current measurement technique?
You forgot fluxgate magnetometers and magneto-resistance based sensors for measuring current non intrusively. So, if you're measurement must be non-intrusive then the resistor is out, as it will introduce power and voltage losses in your circuit etc. However, if you must also measure down to DC then the resistor and Hall effect sensor might be the only choice, but the others are out.
Then there is the complexity consideration vs accuracy required, and closely related the linearity required for the application in mind. Again, a resistor is very suited to linearity and simple (its rather the post-amplifier that introduces the non-linearities etc.). The others are going to add non-linearities at several stages of the measurement.
And finally, if not the last, is the sensitivity (ie S/N) requirements that may or may not just be solved by high amplification.
There may be others but generally it depends on the degree of &quot;intrusivity&quot; your circuit can bare, the complexity, the DC vs AC requirements and the sensitivity requirements (ie S/N). In any case it sounds like you may have already made up your mind for a good reason ...